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Ethical Dilemma - Essay

Ethical dilemmas in business essay

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bill simmons resume Show Your Spirit. Special to Page 2. My bosses at Page 2 gave me a simple assignment this week: Please explain to in business essay the world why Boston fans believe that Roger Clemens might be the Antichrist. You Do! Even the most ardent Rocket-hater would concede that Clemens built a Hall of Fame resumé over the years. Dilemmas In Business! He certainly won enough games -- 265 and counting, including five different 20-win seasons. Resume! He rang up enough K's over that time -- 3,575 and counting, not to mention all of his children who have names starting with the letter K (Koby, Kody, Kodachrome, Kornonthekob and so on). He has more than enough Cy Young trophies (an astounding five), World Series rings (two and counting) and records (including the hallowed Only Guy to ethical essay Strike Out 20 Batters Twice mark). He made enough money over verbs the course of his career to fund a Michael Bay movie -- $60 to $70 million at least, not including endorsements and other goodies. Yup, all the elements are there . except one. He doesn't have any. And that's what makes Clemens so unique, the fact that he keeps chugging along in his late-30s, pitching as well as ever . and yet nobody cares about him. He's like the dilemmas in business essay, Wolf in Pulp Fiction -- no attachment to anyone or anything, a hired gun, a means to job resume ehow an end.

Red Sox fans loathe him. Blue Jays fans despise him. Yankees fans tolerate him, but they haven't embraced him and never will, not with his Boston connections. Who else is left? Can you remember any other superstar athlete squandering his emotional connection to every possible city? Think about it. Name a superstar over the past 30 years; within a nano-second, you instinctively link that athlete to ethical essay a particular place. Rose? Cincinnati. Aikman?

Dallas. Reggie? New York. Rice? San Fran. How Do You Do Essay! Isiah? Detroit. The list goes on in business essay, and on. In every case, the superstar enjoyed his prime years in essay questions hear, a particular city and still reaps the benefits of dilemmas in business essay that relationship to this day. And yet Clemens drifts along, the how do an appendix in an essay, hired hitman, the superstar who sold out his fans for a few extra bucks.

Instead of a team logo, the cap on ethical in business essay, his Hall of Fame statue should simply feature a dollar sign. Of course, the job resume ehow, general public associates Clemens with the city of Boston, regardless of his current Yankees affiliation and enough bad blood over the past few years to rival the Overlook Hotel's main elevator at the end of The Shining. In Business Essay! The prevailing feeling seems to be that Boston fans will soften during the twilight of Clemens' career -- when he enters that cuddly aging and vulnerable stage that turns everyone nostalgic -- and job resume ehow we'll collectively bury the hatchet with him, forgive his sins and accept him back in our good. graces. And then the Rocket will retire, and he'll make the Hall of Fame, and heck, he might even wear a Red Sox cap as a gesture of ethical dilemmas in business essay good will. Contrasts! Well, I'm here to tell you . this will never happen. Sometimes relationships pass a point where they can be salvaged, as Ike Tina, Nicole OJ and Sam Diane all proved over the years. In the Rocket's case, too much has happened. We can't let it go. We won't let it go. When you give your heart to ethical essay someone and they basically drop it on essay questions on roll of thunder my cry, the ground, stomp on it a few times, then ask, What did I do? . well, you don't forget something like that. Ethical In Business Essay! Ever.

In footsteps of job resume ehow Orr, Bird. Clemens splashed onto dilemmas in business, the Boston sports scene in job resume ehow, the mid-'80s -- the zenith of the Larry Bird Era -- causing everyone to ethical dilemmas essay mistakenly assume that the Rocket would follow the footsteps of Bird and Bobby Orr and become our next local sports legend. Orr rejuvenated the Boston hockey scene during the '70s; Bird did the same for basketball in resume, the '80s; Clemens would carry the torch for baseball into dilemmas essay the late-'80s and beyond. Orr . Bird . Job Resume Ehow! Clemens. That's how we were thinking -- this is ethical essay going to happen. Everything felt right about it. Job Resume Ehow! And over the next seven years from '86 to '92, the ethical dilemmas in business essay, Rocket played his part reasonably well -- 136 wins, three Cy Youngs, three playoff appearances and verbs one World Series trip -- but he lacked Orr's panache and ethical dilemmas Bird's sense of The Moment. After awhile, we stopped measuring him against them.

We adored him, we supported him . but we worried about him. You never worried about Bird and Orr. For instance, during Game 6 of the '86 World Series, Clemens could have closed out the Mets and emerged as a genuine hero (you forget this now, but everything was sitting right there at resume content, his fingertips -- legend status, a statue, the whole shebang). He pitched valiantly, holding a 3-2 lead through the seventh before exiting with a blister on the index finger of his throwing hand; even 15 years later, the principles involved (Clemens, former manager John McNamara and former pitching coach Bill Fischer) still argue whether or not Clemens asked out of the game. McNamara vehemently claims that Clemens told him, That's all I can pitch; Clemens steadfastly maintains that he was yanked after the seventh; and prosecutor Jim Garrison claims that there may have been a second pitching coach ordering Clemens to leave the game. Dilemmas Essay! Nobody knows the truth, but we know one thing: Under similar circumstances, Larry Bird would have remained in the game unless he was forcibly removed and hogtied to the Celtics bench. Clemens started eight playoff games in a five-year span from 1986-90, with the Sox winning just one of those starts (Game 7 of the 1986 ALCS against head, a shell-shocked Angels squad). To be fair, Boston's bullpen blew two other potential wins, but only one statistic keeps jumping out: 2-6 . Dilemmas In Business! Not a good sign. We watched Hershiser ('88), Rijo ('90) and Morris ('91) shine in resume verbs, postseasons over that same stretch, quietly waiting for Clemens to ethical embark on job resume ehow, a similar Get on my back, boys run.

Never happened. Eventually we wondered if Clemens only peaked in ethical dilemmas in business, meaningless games, like the time he tossed a complete game shutout during the cover letter, final game of the '87 season (clinching his bid for a second Cy Young) after the Sox had been eliminated from the playoff picture for ethical dilemmas in business essay months. And then there was Oakland ace/nemesis Dave Stewart, who delighted in letter head, beating Clemens in dilemmas essay, their head-to-head matchups (my math might be a little off here, but if I remember correctly, Stewart's lifetime record against head, Clemens was 982-0 -- even the Globetrotters-Generals feud wasn't this one-sided). Things finally boiled over in ethical essay, Game 4 of the essays, 1990 American League playoffs between Stewart and Clemens, as the dilemmas essay, Rocket flipped out while arguing balls and strikes with home plate umpire Terry Cooney and got himself tossed in the second inning, even punctuating his exit by how do an appendix essay throwing a memorable, Whitney Houston-esque tantrum on the field and bumping Cooney more than once. Ethical Essay! Again, Larry wouldn't have done something like that. Our concerns about writing verbs, Clemens deepened after the '92 campaign, when he signed a four-year, $20 million contract and took much of the next 3½ years off, almost like a professor who gets tenure and doesn't feel like grading papers anymore.

Unveiling a historic double chin for the '93 season -- my father's favorite joke that spring was, Would you like another slice, Roger? -- Clemens battled arm problems and floundered to the first losing season of his career. He seemed more dedicated during the strike-shortened '94 season (9-7, 2.85 ERA); unfortunately, he stopped working out that winter and showed up for ethical dilemmas in business essay the post-strike spring training in '95 looking like he was auditioning for the Chris Farley Story. Fueled by essays an increasingly vicious Boston media, Sox fans started to turn against Clemens, especially after his inevitable breakdown during the first part of the season (an extended DL stint) coincided with an improbable playoff run by the Red Sox. Of course, Clemens squandered his only playoff start to the Indians, fueling those can't win the big one doubts. That brings us to '96, the ethical in business, final season of Clemens' aforementioned four-year deal.

Chunky, disinterested and increasingly vocal about Boston's failure to offer him a contract extension, the Rocket turned on the jets once the team fell out of playoff contention, going 6-2 over his last 10 starts and resume verbs striking out ethical dilemmas in business 20 Tigers during a mid-September game at cover, Detroit. Classic Clemens, through and through. You could always count on essay, him when it mattered least (and yes, I'm getting bitter just remembering this whole thing). Understandably, the Red Sox were dubious about essays, signing him to another long-term deal, given that he A) was 34 years old; B) battled health problems in '93 and '95; and C) spent a sizable chunk of the past four years hibernating through his last mega-contract (this was the musical equivalent of U2 asking for dilemmas in business a contract extension from their record company on the heels of Zooropa and Pop). Tensions escalated between Clemens' agents (the hideous Hendricks brothers) and Red Sox general manager Dan Duquette, exacerbated by an appendix in an essay Duquette's steadfast refusal to ethical dilemmas in business essay negotiate during the season or recognize the Rocket's market value. We were headed for contrasts essays a divorce, an ugly one, and the sad thing was this: We knew things were headed that way all along. Dilemmas In Business! Blue Jays, OK, but Yankees . When Clemens ultimately jumped at a $28 million offer to play for the Blue Jays, we were jolted . but deep down, we understood.

Sometimes you just have to verbs move on. So what happened? Why the sudden change of heart? Why did the dilemmas, Rocket practically become the on roll of thunder my cry, modern-day Sirhan Sirhan of New England? Five things happened over the ensuing three-year span that turned Boston fans against Clemens for life; if any of them had unfolded differently, the bad blood could have been averted: 1. The Slap in the Face. When Clemens signed with Toronto and held his first press conference with the Blue Jays, he only ethical needed to take one minute out of the afternoon -- just one -- to say something like this: I want to say something to the Boston fans who stuck with me over the past 12 years: Thanks for all your support. I'll always remember the time I spent in Boston and I'll always be a Red Sox fan at heart. Questions On Roll Of Thunder Hear My Cry! I hope you guys finally win a Series some day and dilemmas I'm just sorry I'm not going to be a part of it when it happens. I wish things didn't deteriorate with the front office, but they did, and I didn't fell like they wanted me around anymore.

And Toronto makes me feel like they want me, and they did everything they could to make me a Blue Jay. For that, I'm grateful, and email resume content I'm happy to be here. But I hope the Boston fans realize that I'll always remember them and I'll miss pitching in front of ethical dilemmas essay them at Fenway. Thanks for 12 great years. You guys are truly special.

That's it. Would have taken about 45 seconds. That's all. Instead, Clemens spent much of the press conference stroking his new Blue Jays hat and showing about as much emotion as Mr. Spock. His only concern seemed to be making everyone aware -- repeatedly, painfully, flagrantly -- of how excited I am to be a Blue Jay and how grateful I am that the Blue Jays have treated me so well.

It was like they offered him an extra 50 bucks every time he praised the Jays. The members of the Boston media kept giving him chances to essays rectify the mistake, repeatedly asking him about his stint in Boston, but Clemens stubbornly stuck to his guns. He was moving forward. He was a Blue Jay. And so he brushed off every question about Boston fans, while we watched in disbelief, our anger mounting. That wasn't just an ethical oversight, it was a hanging curveball right over the plate. (And when we found out that Toronto had offered him the most money -- about $2 million to $3 million more than the defending champion Yankees -- and yet Clemens kept maintaining that he signed with the essay on roll my cry, Blue Jays because he wanted to win a championship . well, that made him a liar, too. Let the record show that Toronto finished 24 games under .500 in ethical dilemmas, Clemens' two seasons above the border.) 2. The Kick in the Gonads. Essays! Suddenly and mysteriously motivated by the slight from dilemmas essay, Boston's front office, Clemens embarked on a rigorous conditioning program during the offseason, determined to prove Team Duquette wrong. He arrived for spring training in essays, superb shape for the first time in eons, repeatedly telling reporters that he had never been better prepared to start a season.

Of course, that revelation should have prompted questions like, If you're so motivated this season, why weren't you as motivated from 1993-96 after signing the most lucrative deal in Red Sox history? and Will you be training with a feedbag and ethical essay a vat of cover chicken wings like you did in '95? but that's a story for another time. Apparently star athletes aren't obligated to essay get themselves in you do an appendix essay, shape until they feel slighted. Anyway, we watched in horror as Clemens rolled off consecutive Cy Young seasons for the Blue Jays. Here were his average stats from '93-'96 in Boston, followed by the '97 and '98 seasons in Toronto: Put it this way: Watching Clemens lighting it up in ethical dilemmas essay, Canada was like breaking up with your girlfriend, then watching her hire a personal trainer, shed 15 pounds, spend 10 Gs on a boob job and join the cast of Baywatch. If that wasn't tough enough to swallow, Clemens thrived against his former team, going 2-0 with a 1.73 ERA in four starts (including a memorable f-you start in Fenway in '97, when he glared at the owner's box after leaving the game) and dropping hints in cover, the papers that Mo Vaughn should join him in Canada. Now it was becoming personal, and when the Boston media started hammering him (with longtime Boston Globe hatchet man Will McDonough leading the pack), the tide shifted against Clemens for good. We felt jilted, we felt used and we started rooting against in business essay, him. Job Resume Ehow! Vehemently. 3. The Revelation.

As luck would have it, at the exact same time Clemens was sparkling for a sub-.500 team in a foreign country, Boston fans were falling for two new heroes: Pedro Martinez and Nomar Garciaparra. Dilemmas In Business! Both of them were blessed with an innate understanding about Boston fans -- what baseball means to us, how we value players who play hard, how we revere players with a sense of email resume content The Moment, how we love when our heroes acknowledge us and essay say things like The fans were great today or Nothing beats playing in Boston in front of these fans. You Do Essay! Sounds stupid? It's not. That's Boston.

We eat that stuff up. The double-barreled emergence of Nomar and Pedro (coupled with Clemens being hooked up to the Rejuvenation Machine in in business essay, Canada) made us realize that the loss of Clemens wasn't as important as we thought. Essays! If anything, the dilemmas in business essay, new guys were more fun to watch. And since Clemens was a self-serving, greedy jerk who didn't care about us when he played here . well, this was war. (If baseball were wrestling, this would be the point where Clemens came into the ring carrying the Canadian flag, shouting epithets about Nomar and Pedro, making unflattering jokes about Boston and forcing everyone to questions of thunder hear stand for the playing of the Canadian anthem. In other words, all ties had been severed -- he was an official Bad Guy.) 4. The Ultimate Violation. After two losing seasons in Toronto, a disenchanted Clemens eventually forced a trade to ethical essay the Yankees in the spring of '99, with help from an resume content illegal You can ask for a trade two years into this deal if you're not happy handshake clause from his contract that drew the ire of the commissioner's office. Ethical Dilemmas Essay! It wasn't bad enough that the winningest pitcher in writing, Red Sox history wanted to play in New York -- he actually cheated to get there. Even the dilemmas essay, staunchest Clemens sympathizers in how do you do an appendix in an essay, New England couldn't defend him anymore. He had crossed over to the dark side. He was Darth Vader with a Texas accent.

He was the ethical dilemmas, enemy. (By the email resume content, way, if you're keeping track, Clemens was officially a quitter, a cheater, a fibber and a traitor at this point). 5. The Final Straw. During the All-Star Game ceremonies at Fenway that same summer, Clemens took part in the Greatest Players of the 20th Century introductions, where every living legend wore the cap of the team with whom they were most prominently associated. Of course, Clemens wore a Yankees hat because he had been playing in New York for a whopping three months. Here was his last chance -- I mean, ever -- to salvage his ties with Boston fans. And he blew it.

At this point, we were like Michael Corleone in in business, Godfather 2 after finding out that Fredo knew Johnny Ola: Fredo, you're nothing to me now. I don't want to see you. I don't want to know you. If you visit our mother, I want to resume writing verbs know a day in advance. You're dead to me. Or something like that. Looking for love. More things happened after the dilemmas in business essay, 1999 All-Star Game; none of them remotely changed the letter, way we felt about the Rocket. Dilemmas Essay! We savagely booed him during an unforgettable Game 3 in the '99 ALCS, when Pedro outdueled him at Fenway and cover letter officially became The Man. When Clemens' wife whined to dilemmas in business the Globe's Dan Shaughnessy about the how do you do essay, treatment her husband had received -- including the infamous quote, I don't know what Roger ever did to them -- that inflamed us even more. Dilemmas In Business Essay! We winced when Clemens finally captured his first-ever ring a few weeks later, taking solace in the fact that the Yankees probably would have won without him.

We enjoyed his battles with Mike Piazza during the 2000 season, including the bizarre bat-tossing incident in Game 2 of the World Series that inadvertently tainted much of the Series for job resume ehow the Yankees and in business essay their fans. Now he's practically old news. The Everyone hates Clemens angle has been done to death. So has the Clemens vs. Pedro angle. And the Fallen hero returns home angle. Done, done, done. Next time Clemens pitches against the Sox, only the Yankee fans in attendance will be cheering him. That begs one final question: Will Roger Clemens ever be loved by any group of baseball fans?

Say what you want about Yankee fans, but at least you know where you stand with them. When they love somebody, they love somebody, especially pitchers. They loved Guidry and Righetti. They loved Cone and Wells. They love Rivera. Writing! But Clemens . Ethical In Business! maybe it's the Boston ties, or the fact that they traded Wells to obtain him, or the way he made them sweat during the '99 stretch run, or his self-destruction at Fenway during the '99 ALCS, or even the bat-throwing incident from last October. Hell, maybe it's a little of everything.

Whatever the case, he hasn't clicked with New York fans; even the most diehard Yankee supporter would admit that. Email! They're cheering him now, but you always get the sense that they're wary of him, that they would turn on him in the drop of a hat. In Business! Watching the movie 61 last month, you couldn't help but notice the similarities between Roger Maris and essay of thunder my cry Clemens -- both All-Star imports who never really won over their fans, through no fault of dilemmas in business essay their own. And so Clemens gives the Yankees a better-than-good chance to resume writing win every five days, and as soon as those odds drop, they'll discard him and ethical find someone else. Those are the stakes. He's a hired gun, a means to an end, a necessary evil. He's a temp.

And maybe he'll end up winning 300 games and job resume ehow another championship ring, and maybe he'll make $25-30 million more before it's all over in business . but everything about those last few years will inevitably feel hollow. How Do You Do In An Essay! He'll have his family and friends in the end. And that's it. The fans will be long gone. As for in business essay Red Sox fans, the job resume ehow, worst part about the ethical in business, Clemens Era is email resume content that void from 1986-1996 -- it's almost like dating someone for an extended time, then suffering through a dreadful breakup that taints every aspect of the dilemmas essay, time you spent together.

It's not that you forget the contrasts essays, good times . you simply choose not to essay think about them anymore, that's all. Job Resume Ehow! There's no point. I remember my then-girlfriend bought me an autographed, limited edition photo of ethical dilemmas Clemens' 20K game back in college, which I dragged with me to every apartment I lived in from 1990-96. After the Toronto press conference, in a fit of rage, I yanked down that picture, never to be seen again. More than four years have passed and that photo is still buried in my bedroom closet. That's what I think of how do you do essay Clemens -- he's stuck in dilemmas, a closet with useless graduate notebooks, eclectic magazines, yellowed photos, letters from old flames and old sweaters that I stopped wearing a long time ago. Is he the Antichrist? Probably not. But I've been following sports for nearly three decades, and no athlete ever let me down quite like Roger Clemens did.

Fortunately, we can take solace at an appendix essay, the potential sight of Clemens standing on the field at New Fenway, maybe 40 years from now, being introduced on ethical, Old Timer's Day 2041 . and getting showered with boos from Red Sox fans. I can't believe they still haven't let this go, he'll mumble to himself, a thin smile spread across his face, oblivious to the bitter end, still waiting for the fans to come around.

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Ethical Dilemma - Essay

Graduate School Advice Series: 10 Things You Should Know Before Starting A PhD. From a senior PhD student to dilemmas in business essay, a starting PhD student, this is the graduate school advice nobody will tell you but that you need to succeed and contrasts, get your PhD title. We all join graduate school with rainbows and essay, butterfly ideas in our minds. We will cure cancer, do research in interesting topics, learn a lot, oh! the scientific method, meet smart people. Guess what? Life as a PhD student is head much different. Here’s what I discovered during my PhD that was totally different from what I had imagined.

This is my graduate school advice for new PhD students. Graduate School Advice 1: Your #1 Goal Is To Publish Peer Reviewed Articles. Assuming that you want to finish your PhD and become a “doctor”, you have to publish peer reviewed articles. This is the one thing that if you do, you will get your title hands down. Isn’t the goal to be an expert in ethical dilemmas in business your field? Being an expert without peer reviewed publications equals to being an expert without a PhD. Click to tweet.

It sounds materialistic, specially when compared to this romantic idea of doing science for essay questions of thunder my cry, the progress of human knowledge. Sadly it is how the ethical in business game is cover head played. This is the rule. Ethical In Business? Publish or perish. People are trying to change the essay questions hear my cry game with Open Access, Open Data, Open Science, and writing their results in dilemmas blogs (if you do not have one, start a science blog right now). Contrasts Essays? These are all very needed initiatives that are changing the scientific game. But still, in order to win the in business game you need publications (in The Netherlands, where I do my PhD, you need 4).

So the best graduate school advice you could get is write, write, and write some more. Graduate School Advice 2: The Most Difficult Part Is To Stay Motivated. Since a PhD involves diving very deep into a topic, one might expect that learning very complicated stuff would be the on roll hear hardest part. If you don’t learn fast enough and well enough, you will not finish your PhD. Right? Not true. The most likely reason for dilemmas in business, not finishing a PhD, despite not having publications, is resume content … don’t laugh … quitting your PhD.

Click to tweet. What can make you quit your PhD? It happens usually half way a PhD’s duration. You won’t feel you had enough progress. You will be lost in the middle of an ocean of uncertainty. You will still have in front of you a couple of painful years to dilemmas in business essay, endure. Resume Verbs? The alternative of a bigger pay-check in industry will look really tempting at that point. That period is called the Valley Of Shit or the Phase 3 of PhD Motivation, the “Crisis of Meaning” . Almost every graduate student goes through this existential crisis. You just need to realise that it happens to everybody and that you can overcome it. Dilemmas Essay? Focusing on constant little progress helps more than evaluating if a bigger goal has been achieved.

Something that worked for me was to start your science blog and share with others my experiences (see how a science blog saved my PhD). It helps to put all your troubles in job resume ehow perspective. If you need help starting a science blog and dilemmas essay, growing your academic footprint check our videotutorial. Graduate School Advice 3: You’d Better Finish Your PhD Fast. As you see it sucks to quit your PhD half way. Such a waste of time for going away without a PhD tittle. Do you know what sucks even more? To spend 4, 5, 6 years and not finish your PhD. Contrasts Essays? Ouch!

I have seen this happening to dilemmas, many people and it has to do with two causes. One, you realise a bit, just a bit, too late that this is not going to resume writing verbs, work. Seriously, do you really need 5 years to decide you won’t have enough results and papers to ethical dilemmas in business, defend your thesis? Please, evaluate every 6 months if you are still on track, if you are going to make it and correct direction if needed. In a PhD you should track progress and correct direction regularly, don’t wait till it is too late. Click to tweet. Two, after 4 years you are almost there, you have enough data to write those two last articles and the introduction of your thesis. Job Resume Ehow? It feels so close and obvious you are going to ethical dilemmas in business essay, get your PhD title that you decide to essays, start a postdoc or a new job. Excellent Wrong choice, Sir. The stress and ethical dilemmas essay, pressure to integrate in the new position won’t leave enough room for you to write those last pages.

Sure, you are Superman and you are going to contrasts essays, write after dinner and during the weekends. I have seen many people failing at this to believe it is a good strategy. So finish your PhD fast and on ethical dilemmas essay, time, avoid delaying it. And please, do not start new job until you really finish your PhD. Graduate School Advice 4: You Are The Expert In Your Field Of Research.

We all regard our supervisors, principal investigators and how do you do an appendix essay, promotors as a source of ethical dilemmas in business essay, infinite knowledge. They are like superhumans. One common source of frustration is to ask your PhD supervisors for help and realise they know as much as aunt Martha does. If these brilliant guys can’t answer your problems, how are you expected to answer them? This is why you are here. Verbs? To answer those questions your bosses cannot answer. At the end of dilemmas essay, your PhD you should be the expert on your topic, and cover letter head, not your professor. Click to tweet. You can very well approach your superiors with a problem and propose several solutions. Give arguments for ethical dilemmas in business essay, each one. In this context, they might be able to use their scientific instinct, the so called educated guess, to give you a hand.

Graduate School Advice 5: You Won’t Make A (Big) Dent In The Universe. We know you are not in graduate school for the money. Probably you want to contribute to the knowledge of mankind, fix a problem or discover something new. Fair enough. The sad truth is that for job resume ehow, the majority of essay, PhDs, their research will get noticed and used by a handful of other researchers. And that is fine. Letter? Most of scientists make big contributions after a lifetime of in business essay, research, not in a couple years. The contribution of your PhD to science will be as noticeable as a fart in the middle of a tornado. Click to tweet. Then why do it a PhD in the first place?

Well, you need to job resume ehow, start somewhere and a PhD can give you the tools and skills necessary for achieving higher scientific goals. Graduate School Advice 6: Key Skills In Graduate School: Reading, Writing, Networking. In kindergarden you learn to read, write, paint and play with other children. Ah those relaxed days when your only ethical in business essay worries were choosing the colour of the crayon or if you were going to head, play hide and in business, seek. Graduate school is the essays kindergarden of scientists. You learn again to read, write and ethical dilemmas essay, interact with others. Click to tweet. That’s what you need to learn as a PhD school.

Reading: you need to verbs, skim over a scientific paper and in essay a few seconds decide if you should invest the next 30 minutes reading it in content depth. If you do, you should easily find what is the novelty of the research presented, if it can be useful for your work, and how does it compare to ethical dilemmas in business, what you are doing. Contrasts Essays? Writing: in academic papers you need to get to essay, the point. You need to be comprehensive and concise at the same time. You need to be technical yet readable. Email Resume Content? And if your mother tongue is in business not English you should work hard not to sound like Google Translate. Networking: although some scientists would love to email resume content, work in ethical essay a cave away from the essay questions of thunder hear my cry rest of the essay community, you should interact with other peers. Networking can bring you possible collaborators and chances of writing more papers, your new postdoc position, new ideas, or understanding form fellow PhD students that are also going through the Valley of Shit. Graduate School Advice 7: Pimp Your Online Reputation And Grow Your Academic Footprint. Traditionally scientists would grow their network and get exposure by publishing papers and verbs, attending conference.

In this new world, a great piece of graduate school advice is to take care of your online presence. A PhD student should take care of dilemmas, his online reputation from you do, day 1. Click to tweet. While you should still do these things during your PhD, you could make use of some digital tools to be a better scientist and to grow your online reputation, visibility and in business, academic footprint. There are 3 key online tools that you can use to email content, grow your online presence as a scientist: a science blog, Twitter, and LinkedIn, aka the social media trinity for scientists. If you use these three tools you will stop being invisible for Google.

People will find you and discover what your research is about. You can use a science blog to share your opinion about your field of ethical dilemmas in business, research. You can also share materials like posters and presentations. Questions On Roll Of Thunder Hear My Cry? Or even a description of your papers in simple words. With Twitter you can connect with fellow scientists, share your news and also discover new research related stuff.

LinkedIn can become your online CV, a place where others can easily see your skills, publications and ethical dilemmas, education. In Next Scientist we are crazy about the digital world, but do not forget to letter head, transfer some of these online relations to the physical world. Try to meet face to face with some of in business, your online buddies, either invite them to visit your group, go for a coffee, or arrange that you will meet in a scientific conference. Graduate School Advice 8: Time Management Rules From The 4 Hour Workweek That Change The Game. If you haven’t read The 4 Hour Workweek yet, buy it, devour it and contrasts, apply it to ethical in business essay, your PhD. It is stuffed with great ideas that you can turn into writing verbs, graduate school advice, it will revolutionise the way you see the world. You want to be effective, not just efficient: being efficient at ethical dilemmas in business essay, something unimportant is useless. Being effective at finishing important things makes a big difference. Pareto’s Law 80/20: focus your efforts in letter head that 20% of tasks that bring 80% of the ethical in business essay benefits (like writing papers).

Remove the 80% of cover letter head, tasks that only contribute to 20% of the results (like revising constantly your time management system). Ethical Essay? Parkinson’s Law: set tight deadlines, the how do essay last minute rush will activate your creativity. If you decide you can do a task in ethical essay 2 days, guess what? It will take your 2 days to you do, accomplish it. If you would assign 3 hours to essay, it, you would still finish it. You are scared, so is everybody else: when talking to other people, giving presentations, applying for that position, it is scary, but everybody else would be scared.

Have near-impossible goals: these are the goals that motivate you and that are worth working hard and walking the extra mile. Job Resume Ehow? When would you work harder? When you have to prepare a poster for a regional meeting or when you have to give a talk at an international conference in New York? I thought so. Graduate School Advice 9: Deliver Fast And Often, Get Feedback. A great piece of graduate school advice I got when I started was:

At the start of a PhD get some little results fast to boost motivation, don’t go first for big results. Click to tweet. This is great advice because having some small results will a) give you a sense of progress, so your motivation will go up and b) give you something to present (maybe as a poster) and discuss with other scientists. In your daily work, you should aim at “good enough” and “deliver soon” instead of “perfect delivered in a few more days” . Dilemmas Essay? If you deliver intermediate results or a draft of a paper, you have the chance of getting feedback soon and correct your direction if needed. Bear with me: done is better than perfect . Don’t wait till you have the perfect figures or till you are not ashamed of the contrasts quality of your work. You need to make progress and you need the feedback of your supervisors to dilemmas in business, do so. Get rid of your shyness and “move fast, break things, deliver, ship” on a daily basis. Graduate School Advice 10: Enjoy The Ride. The graduate school advice we shared might sound a bit too harsh. We just want to point out how a PhD really is, so you are not surprised later on. But do not let this discourage you.

Graduate school has many perks that make it a great experience . Email? You will meet interesting people and you will have the chance to ethical in business essay, explore your own ideas and to be creative. Remember that you are still a student, so enjoy life like a student. Do not take everything too seriously and cover letter head, make use of dilemmas in business, your free time. In some cases you might get a salary or stipend. Isn’t it great to be a student but with money? For those cases where you don’t get paid or your salary is microscopic, you can easily make a second income in graduate school and enjoy the life of how do you do essay, a student. You have the chance to travel. Get results and present them in conferences. Ask your boss to pay for ethical dilemmas, the trip or apply for a travelling stipend for students. Find collaborators and get them to invite you to visit their lab. Graduate school is a great time, make good use of your chance of resume writing verbs, being here.

Now you know how it really is at graduate school. You have almost everything you need to ethical dilemmas, succeed in your new PhD life. What’s missing? You will find in the following posts of resume, these series. Thinking Of Applying to essay, Graduate School?

Check These Sample Letters For Graduate School. When applying to graduate school you are going to submit several letters. The goal is to essays, give a good impression and get invited for an interview. You should adapt to your needs a sample letter that has been successfully used. [note color=”#efdcde”]Check our letters for graduate school, which include a statement of purpose for graduate school and ethical dilemmas in business essay, a recommendation letter for head, graduate school . You can get the letters for graduate school here.[/note] Additionally you can get sample letters you will need throughout graduate school, for ethical, instance when you are submitting your first scientific paper to a journal or when you are applying to a scientific conference. Do you want to be better at Academic Writing? Is “Write Better Scientific Papers” one of your goals? Do you have trouble writing your PhD thesis? If the answer is yes, I have something good for you.

Keep reading.. She has helped hundreds of how do essay, scientists to write better, specially PhD students. Ethical Dilemmas In Business Essay? She knows exactly where you are struggling with your academic writing. With this course you will be able to: learn how to ban procrastination and stay on essays, track with your writing project. Dilemmas? finally complete a chapter of your thesis in job resume ehow just a few weeks. draft your paper without struggles or anxiety. improve your productivity and experience a sense of real achievement. write efficiently without wasting hour upon in business hour. gain confidence and enjoy your writing project. If you want a summary of the details of the course, this is what you will get: All the questions of thunder academic writing know-how you could image delivered via video in easy to follow modules. Worksheets and templates so you don’t have to ethical in business, start writing from scratch. Supporting materials to create tables and figures, because an article is not just text. Plenty of bonus materials (for instance on productivity) for the academic writing die-hards out there. The response from everyone has been incredible. This is the course I wish I had followed at the beginning of my PhD.

Julio Peironcely, PhD is the founder of Next Scientist and a PhD by Leiden University. He helps PhD students to stay motivated, be more productive and finish their PhDs. Follow him on Twitter (@peyron) or read more from him on job resume ehow, JulioPeironcely.com. These advice all could not be more right, however, I have been wondering whether knowing these would or could make difference. If the ethical dilemmas in business essay answer is a “Yes”, it makes sense, of job resume ehow, course; if a “No”, then what else? What really matters if I wanna be better, far better than what I am for the time being? Are we relevant and do we make a dent?

Some do, but I do not think it is a drawback or problem. Ethical Dilemmas In Business? The point is hear my cry research is an intellectual pursuit that some enjoy. When a friend of in business essay, mine retired, he said he had worked all his life on these novel compounds but, after all, the great applications never came and he said he was disillusioned by it all. My response to him is that it is essay hear my cry not necessary to make a dent. Ethical Dilemmas In Business Essay? All we need to job resume ehow, do is maintain knowledge and pass it on. Ethical? Somewhere down the line, one of the students will make a dent. I recall when a large gov. lab closed. The expertise lost and you do essay, it would take 5 years minimum to ethical dilemmas in business essay, recreate that synergism the day after everyone dispersed. Point is resume writing verbs enjoy your research, try to make a dent but if you do not, be content that we are little cogs in the knowledge wheel and success comes in many forms. There is ethical in business essay nothing wrong in passing on what you know. great points and very inspiring.

Thanks a lot for sharing. Thank you, very well stated… we are cogs in the wheel of knowledge.. ! Besides, I can not imagine why anyone would consider himself / herself as unsuccessful. Success in letter head research is not in proving what you thought was right. Success, often is in finding the right track for ethical, oneself and others. In your particular example, least of all others would know that those ‘novel compounds’ were either not promising, or had to how do in an essay, have that little bit of a ‘different something needed to them’, and in business, whoever will find that, will recognise the importance of the contribution his/her predecessors made. Resume Verbs? Or so I think.

Maintain knowledge and ethical dilemmas essay, pass it on how do an appendix in an essay, … that’s really good advice. Dilemmas Essay? That’s setting the right expectations. Email Resume Content? Wanting to make a dent in the universe can lead to severe frustration. More often than not we only hear the stories of those who make a dent, who more often than not, are the exceptions. that great advice for any new blogger. The biggest problem is there are no jobs for you when you finish. Even if you get a postdoc job progession from their is ethical dilemmas statistically very unlikely, you’ll be a glorified tech at best. Hey check these posts: I have just stopped by to you do, give some feedback:

I was not even looking for ethical essay, tips for grad school application but I found myself reading this blog. Head? It seems your google trick worked perfectly and you are also a good “writer” that your writing skills made me read all of ethical dilemmas in business, it. Indeed, I will apply for some phd positions in the near future. So, maybe see you around Leiden in a workshop. Hey T, thanks for contrasts essays, your comment. Dilemmas In Business? Good luck with PhD hunt. So sad that it’s not about doing good science… In total agreement. Email Resume Content? Yet this article is accurate in its interpretation of current standards within the dilemmas scientific community. As per Advice No.1, 5, 6, 7 and 9: Its fundamentally wrong that people spin, pimp and gloss their research just to get published. To me these publications reflect poorly of their authors.

As for publishing 4 papers in job resume ehow 4 years of PhD study…well I think this encourages too many irrelevant publications with too narrow a scope, and ethical in business, likely of you do an appendix in an essay, little contribution to science. “Being an expert without peer reviewed publications equals to being an ethical in business essay, expert without a PhD” – This of course is true. But taken with the 4 publications in 4 years comment, if everyone is publishing limited and well spun/written work but of little scientific value then the education level drops, with continually lesser and lesser quality of scientist (or researcher) becoming peers. We should encourage people to publish only when they are ready, and as little as they wish, with the understanding their own careers/reputation are at risk if they do not produce. I prefer this philosophy over “publish or perish” because it encourages quality rather than quantity. “As for publishing 4 papers in 4 years of PhD study…well I think this encourages too many irrelevant publications with too narrow a scope, and likely of little contribution to science.”

I think that big contributions to science rarely come from PhD students. Thos happen later on in their scientific careers when they manage to run labs with big groups. Then impactful publications are possible. “We should encourage people to publish only when they are ready, and as little as they wish, with the understanding their own careers/reputation are at risk if they do not produce. ” Who would be interested in how do in an risking career and reputation in exchange of publishing little? not many. With such a big risk we would have very few PhDs.

In the current system, where armies of dilemmas in business essay, PhDs sustain the research in resume verbs universities, the system would collapse. Thanks. Dilemmas In Business? I would mention pick great tools like Mendeley, Evernote, Zotero or bohr.launchrock.com. Great thanks! I would advise using a good reference tool like Endnote, Mendeley or bohr.launchrock.com. I graduated with a Bsc in Electrical Engineering when I was 23, back then I wanted to pursue my master and Phd. Cover? I went off the track a lil and I am not 26 and ethical dilemmas essay, have a decent paying job. However, the how do an appendix in an I constantly think about quitting my job and going back to school to dilemmas in business, do my graduate school ’till I get my Phd and dedicate my life for science and engineering. Questions On Roll? Is it too late for me (being 26)? I started my PhD when I was almost 26. I have seen people starting (and finishing) PhDs at older ages.

If you think doing science is your call, go for it! I have another question regarding the “age issue”, since I have been somewhat worried for the last weeks and dilemmas in business, your advice could well help me. I completed a BSc in Manufacturing Engineering in 2010, then a MSc in Mechanical Engineering in 2011 and I have been working for how do essay, a private company since then. Now I have just turned 27 (in Spain BSc’s take 6 years…) and I think that academia is what I should be doing for ethical in business, the rest of my life. Do you think it is way too late to have a chance to succeed? I think age won’t be a problem as long as you are good at contrasts, it and in business essay, work hard. I hope it won’t, thank you for your reply #128521; My advice to you GPC and Khalid is do not rush into a PhD now because you are worried about your age. Have a look around, but wait until the writing right PhD, not simply the first PhD, comes your way. If you have started the wrong PhD and ethical essay, that is clear to you now, maybe you should quit (less than year one) or try to change it (more than year one).

I began a PhD which wasn’t suitable for cover head, me partly due to a fear I was getting too old, and I currently believe that was a mistake. If the right choice is not available for you now then I hope you enjoy the ethical in business one you do select. I wish you good fortune! I am a 33 yr old woman with 2 kids pursuing my Masters and PhD. In An? Believe me age does not matter; experience does #128578; and also of course hard work. If you are sure this is your calling, don’t let ‘age’ stop you. I completely AGREE…I am a full-time employee, a wife, and mother of 2 kids and ethical in business essay, although I completed my Bachelors in 1997, I’ve just completed my Masters degree this year at job resume ehow, the age of 37 and I am considering applying to ethical in business essay, a PhD program as well. The whole thing is, the job resume ehow choice or timing of going to school will vary because grad schools will consist of EXPERIENCED individuals from all walks of life and in various stages of life…it’s not like undergrad where students are fresh out of high school for the most part which even nowadays, there are adults starting a Bachelors program at age 22-24 minimum. I wouldn’t get hung up on dilemmas in business essay, age just the INTEREST and desire in achieving your goal or vision and gaining what you want. Whether you complete a graduate program at 19 or 60 is not the factor…it’s completing the how do in an essay program SUCCESSFULLY that matters. Of course not.

Some students go straight into in business, grad school after completing their undergraduate studies, and others become part of the work force to email, even determine if they want to pursue a grad degree in the field they began, or some individuals start to work AND get married and start families before enrolling and dilemmas in business, completing grad school (me). School is contrasts always there and grad programs/post grad programs will consist of a population of students of ALL ages at various points in their careers/lives or they are in ethical in business essay the midst of a career transition. One person that truly inspired me is my friend’s mother who completed her master’s degree and continued to complete her PhD in her 60’s and she has enhanced her career as a result. Essay Questions Of Thunder Hear My Cry? In other words, while you still have a life and in business, interest, don’t let age be a factor…..just go out and do it. I am just 43 #128578; graduated at contrasts, 24 and mastered at dilemmas in business, 28. Could not find a PhD supervisor in job resume ehow my field in my country, so could not pursue it. Ethical In Business Essay? Now I have an opportunity that I could start in in the following years, so already thinking about it. I know at job resume ehow, least one person, a farmer by profession, from the ‘ill famed’ Pakistan, who did his PhD at an age of post-60, from a niche ‘Agricultural University, Faisalabad’. He did not need a PhD for a new job, nor would he get promoted in anyway in ethical dilemmas in business his current ‘career’, but thirst for knowledge has no bounds. He is at email, least in part a reason I am still interested in a PhD.

Now it is ethical dilemmas your call to choose,or not to choose, to be older than 60 at essays, 26. Don’t do it. Leaving a job for grad school is the biggest regret of my life. Is there anything about the Phd process that encourages perfectionism in ethical dilemmas particular? I’ve noticed that Phd graduates (working in govt/industry) tend to spend excessive amounts of how do an appendix, time on minute details early on in a project, resulting in the last part of a project being too rushed and often either missing deadlines or making major errors, when simply having a “drop-dead” date that allowed reasonable time for the later parts of the project would have prevented this. Hey anon, I am with you here. Most of essay, us get a deadline: a thesis in writing 4 years. Having intermediate deadlines along the way will help to finish on in business essay, time. Writing? If nobody (aka professor) sets deadlines for you, do it yourself. I’ve enrolled as part time, self -funded . And spent first year but still have not find a topic ? still no sense #128577; I liked your Blog….It spoke about most problems faced and good strategies to combat them..Also delivering good enough results quickly v/s perfect ones strikes home cause I procrastinate and make excuse to myself oh i’ll make it better but am just wasting time….

Thanks for writting the article #128578; Tell me about wasting time!! I am a pro. Thanks Julio. Not all advice need to ethical in business essay, be correct or to cover head, fit everyone. In Business Essay? I am not even evaluating.

If nothing else, this article is brilliantly written, with a funny twist to the most serious issues. Every negative thing is cleverly wrapped in and concluded with positivity #128578; I am glad I have read it. Thanks again. God Bless you! Thanks for email resume, your words Laeeq, that’s kind of you.

“will TALL you”? And this author has a PhD? Hey Jessica, thanks for finding a typo and kindly letting me know. There is just ONE thing you should know before starting a PhD. In Business Essay? DO YOU REALLY LOVE WHAT YOU DO? There are no tips, no secrets, no magical formulas. subscribed to this (twice) and got the emails too, bot no mention of any ebook . after a year, i decided to drop out of my phd program. i have a masters and for job resume ehow, what i do, there was no real benefit to getting one.

i DON’T want to spend my life in academia. i did a little video with my reasons why. Ethical Dilemmas Essay? http://amandafrances.com/phd. PhD students don’t make theses, but rather dissertations. A bit of advice that I wanted was. Cover Letter? I live in Pakistan and I am interested in Biology. Dilemmas Essay? I have just completed my Alevels and resume writing, I am looking for a Bachelors programme.However at this stage in life I am feeling terrified and anxious. I always though I wanted to do a Phd in dilemmas Biological sciences. Resume Verbs? However Now due to being constantly scared I am unsure what I want to do. Ethical Dilemmas In Business Essay? Therefore I want to ask whether I should continue and do my BS in applied biosciences or do something else?

Also are there ANY other WELL paying job options for a BS applied biosciences other than going into research? Also can I get a masters in business or finanace or marketing after my BS in appliedbiosciences (from a good uni) if I decide to go down another path afterwards? Dear , i read all this. its really informative, and might reflecting , whats that’s really all this is. actually i am new, just going to complete MS. now at the moment trying and throwing emails to a wide range of professors for PhD supervision. i would be very glad and thankful, if you could give some clear direction, suggestion and some motivation. my interest area is text mining, machine learning and job resume ehow, bioinformatics. thanks once again. […] 10 ????? ??? ??????? ??? ?? ???? ????????? 10Things you should know… […] […] read an interesting blog about living through a PhD that had something about the Four Hour Work Week which looks pretty cool. It also gave me a few […] […] Graduate School Advice: 10 Things To Know Before Starting A PhD […] […] to Make It Through the ethical dilemmas First Year of a PhD Program in One, Albeit Frazzled Piece Graduate School Advice Series: 10 Things You Should Know Before Starting a PhD Program PhD Program Success and Survival […] […] 10 Things you Should Know Before Starting a Ph.D. […] […] * 10 Things You Should Know Before Starting a Ph.D. […] […] Scientist has already a post on using goals, but it never hurts to repeat.

The point of the goals is to cover letter head, help you prioritize and increase […] […] Graduate School Advice: 10 Things To Know Before Starting A PhD says: February 24, 2015 at 8:36 am […] […] Related links The Thesis Whisperer blog and e-book has awesome tips on time management and productivity in dilemmas in business general (best $3.99 I ever spent). Same goes for Get a Life, PhD blog. Conservation Bytes recently laid out the top 5 skills for email content, grad students here, as does Next Scientist here. […] […] Graduate School Advice Series: 10 Things You Should Know Before Starting A PhD […] […] Graduate School Advice: 10 Things To Know … – You are here: Home / Graduate School Advice / Graduate School Advice Series: 10 Things You Should Know Before Starting A PhD […] […] intellectuals that to get ahead, they must make a name for themselves early on by networking, “pimping their online profile,” and making themselves relevant even beyond the bounds of higher […]

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Algebraic Number Theory - Essay - Mathematics. Algebraic Number Theory. Version 3.03 May 29, 2011. An algebraic number field is dilemmas in business essay, a finite extension of Q; an algebraic number is an element of an algebraic number field. Algebraic number theory studies the arithmetic of algebraic number fields — the ring of integers in email the number field, the ideals and units in the ring of integers, the extent to which unique factorization holds, and so on. An abelian extension of a field is a Galois extension of the field with abelian Galois group. Class field theory describes the abelian extensions of a number field in terms of the arithmetic of the field. These notes are concerned with algebraic number theory, and the sequel with class field theory. v2.01 (August 14, 1996). First version on the web. v2.10 (August 31, 1998). Fixed many minor errors; added exercises and an index; 138 pages. v3.00 (February 11, 2008). Corrected; revisions and additions; 163 pages. v3.01 (September 28, 2008).

Fixed problem with hyperlinks; 163 pages. v3.02 (April 30, 2009). Fixed many minor errors; changed chapter and page styles; 164 pages. v3.03 (May 29, 2011). Minor fixes; 167 pages. Available at www.jmilne.org/math/ Please send comments and corrections to me at ethical, the address on my web page. The photograph is of the Fork Hut, Huxley Valley, New Zealand. Copyright c 1996, 1998, 2008, 2009, 2011 J.S. Milne. Single paper copies for job resume ehow, noncommercial personal use may be made without explicit permis- sion from the copyright holder. Notations. . . . . . . . . . . . . . . . Dilemmas In Business Essay. . . . . . . Essay Questions On Roll. . . Dilemmas In Business Essay. . . . . . . . . . . . . . . . 5 Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Email. . . . . 1 Exercises . . . . . . . . . . . . . . . . . Dilemmas Essay. . . . . . . . . . . . . . . . . . . . . . 6. 1 Preliminaries from Commutative Algebra 7 Basic definitions . . . . . . . . . . . . . Essay On Roll Of Thunder. . . . . . . Dilemmas In Business Essay. . . . Letter. . . . . . . . Ethical Dilemmas In Business Essay. . . . . . . 7 Ideals in products of rings . . . . . . . Cover Letter Head. . . . . . . . . . . . . . . . . . . . . . . . 8 Noetherian rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Noetherian modules . Ethical Dilemmas In Business. . . . . . . . . Resume Writing. . . . . . . Ethical In Business Essay. . . Letter Head. . . . . . . . . . . . . . In Business Essay. . . . Cover. 10 Local rings . . . . . . . . . . . . . . . . . . . . . . . . Ethical. . . . . . . . Contrasts. . . . . . . 10 Rings of fractions . . Ethical Dilemmas. . . . . . . . . . . . . . . . . . . . You Do An Appendix In An Essay. . . In Business Essay. . . . . . . . . . . . 11 The Chinese remainder theorem . . . . . . . . . Cover Head. . . . . . . . Ethical In Business Essay. . . . . You Do An Appendix In An Essay. . . . Dilemmas Essay. . . . 12 Review of tensor products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Exercise . . . . Job Resume Ehow. . . . . . . . . . . . . . Ethical Essay. . . . . . . Essays. . . . . . . Essay. . Content. . . Dilemmas In Business. . . . . . . . 18. 2 Rings of Integers 19 First proof that the integral elements form a ring . . . . . . Letter. . . Ethical Essay. . . . . . . . Writing Verbs. . . . 19 Dedekind’s proof that the integral elements form a ring . . . . In Business. . . . . . . . . . . 20 Integral elements . . . . . . . . . . . . . . . . Email Resume. . . . . . . . . . . . . Dilemmas In Business. . . . . . . 22 Review of bases of A-modules . . . . . . . . . . . . Essays. . . Dilemmas In Business Essay. . . . Content. . . . . . . . . . . 25 Review of norms and traces . . . . . . . . . . . . . . . . . . . . . . . . Dilemmas In Business. . . . . . 25 Review of bilinear forms . . . . . Email Resume. . . . . . . . . . . . . . . . . . . . . . . . . . 26 Discriminants . . . . Ethical Dilemmas Essay. . Content. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . In Business Essay. . . Job Resume Ehow. 27 Rings of integers are finitely generated . . . . . . . . Dilemmas Essay. . . . . . . . Job Resume Ehow. . . . . . . . . 29 Finding the ring of integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Algorithms for finding the ring of integers . . . . . . . . . . . . . . . . . . . . . 34 Exercises . . . . . . . . . . . . . . . . . . . . Ethical In Business. . Resume Verbs. . . . . . . . . . . . . . . . . . 38. 3 Dedekind Domains; Factorization 40 Discrete valuation rings . . . . In Business Essay. . . . . . . . . . . . . . . . . . . . . . . . . . You Do An Appendix In An. . . 40 Dedekind domains . . . . . . . . . . . . . . . . Ethical. . . . . . . . . . . . . . . . . . You Do An Appendix In An Essay. 42 Unique factorization of ideals . . . . . . . . . . . . . . Ethical. . . . . . . . . Head. . . Dilemmas Essay. . . . . 43 The ideal class group . Job Resume Ehow. . . . . . . . . . . . . . Ethical. . . . . . . . . Email. . . . . . . . . . . 46 Discrete valuations . . . . . . . . . . . . . . . . . . . . . . In Business Essay. . . . . . . . . . . . 49 Integral closures of Dedekind domains . . . . . . . . . . . . . . . . . . . . . . . 51 Modules over Dedekind domains (sketch). . . . . . . . . . . . . . . . . . . . . . 52.

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Job Resume Ehow. . . . . . . . . . . . . . . 68 Some calculus . . . . . Ethical Dilemmas Essay. . . . . . . . Resume Verbs. . . Ethical Dilemmas In Business Essay. . . . . . . . . . Contrasts. . . Dilemmas Essay. . . . . . . . . . Job Resume Ehow. . . 73 Finiteness of the class number . . . . Ethical In Business. . . . . . . . . . . . . . . . . . . . . . . . 75 Binary quadratic forms . . Job Resume Ehow. . . Ethical Essay. . . . . . . . . . . . . . . On Roll Hear. . In Business. . . . . . . . . . . An Appendix. . . 76 Exercises . Dilemmas In Business. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Head. . . . . . 78. 5 The Unit Theorem 80 Statement of the theorem . Dilemmas. . . . . . Cover. . Dilemmas. . . . . . . . . . Job Resume Ehow. . . . . . . . . . . . Dilemmas Essay. . . . 80 Proof that UK is finitely generated . How Do You Do An Appendix Essay. . . . . . . . . . . . . . . . . . . . . . . . Ethical Essay. . 82 Computation of the rank . . . . . . . . . . . . . . . Job Resume Ehow. . . Essay. . . . . . . . . . . . . . 83 S -units . . . . . . . . . Email Resume Content. . . . . . . . . . . . . . . . Essay. . . . Email Resume Content. . . . . . . . . . . . . Dilemmas In Business. . 85 Example: CM fields . . . . . . . . . . . . . . . Questions On Roll Hear. . . Ethical Dilemmas In Business Essay. . . . . . . You Do. . . . . . . . . . . 86 Example: real quadratic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Example: cubic fields with negative discriminant . . . . . . . Dilemmas In Business. . . . . . Email Resume. . . . . . 87 Finding .K/ . . . . . . . . . . . . . . . . . . . . . . . . . . Ethical Dilemmas Essay. . . . . . . . . . . 89 Finding a system of fundamental units . . . . . . . . . . . . . Essay. . . . . . . . . . . 89 Regulators . . . . . . . . Ethical Dilemmas In Business. . . . . . . . . . . . Questions My Cry. . . . . . . . . . . . . . . . . . . . 89 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dilemmas Essay. . . . 90. 6 Cyclotomic Extensions; Fermat’s Last Theorem. 91 The basic results . . . . . . . . . . Job Resume Ehow. . . . Ethical. . . . . . . . . How Do Essay. . . . . . . . . . . . . . . 91 Class numbers of cyclotomic fields . . . . . Ethical In Business Essay. . . . . . . . . . . . . . . . . . . . . 97 Units in cyclotomic fields . . . . . . . . How Do You Do In An. . . . . . . . . Ethical Dilemmas In Business. . . . . . . . . . How Do In An. . . . . . 97 The first case of Fermat’s last theorem for regular primes . . . . . . . . . . . . . 98 Exercises . . . . . . . . . . . Dilemmas Essay. . . . . . . . . You Do An Appendix Essay. . . . . . . . . . . . . . . . . . . . 100. 7 Valuations; Local Fields 101 Valuations . . . . . In Business. . . . . . . . . . . . . . . Cover Letter Head. . . . Ethical Dilemmas In Business Essay. . . . . . . . . An Appendix In An Essay. . . . . Dilemmas In Business Essay. . . Resume Content. . . 101 Nonarchimedean valuations . . Dilemmas Essay. . . . . . Email Resume. . . . . . . . . . . . Ethical Dilemmas In Business. . . . . Resume Writing Verbs. . . . . . . . 102 Equivalent valuations . . . . . Ethical Dilemmas In Business Essay. . . . Contrasts Essays. . . . . . . . . . . . . . Ethical Essay. . . . . . . . . . . . 103 Properties of discrete valuations . . . . . . . . . . . . . . . . . . . . Questions Of Thunder My Cry. . Ethical Dilemmas In Business. . . . . . 105 Complete list of valuations for how do an appendix essay, the rational numbers . . . . . . . . . . . . . . . Essay. . 105 The primes of a number field . . . . . . . . . . . . . . . . How Do An Appendix In An Essay. . . . . . . . . . . . Essay. . 107 The weak approximation theorem . . . . . . . . . How Do You Do An Appendix In An Essay. . . . . . . . . . . . . . . . . 109 Completions . . . . . . . . . . . Dilemmas. . . . . . . . . . . . . . . Resume Writing Verbs. . . . . . . Ethical Essay. . . . . . . 110 Completions in the nonarchimedean case . Verbs. . . Ethical In Business. . . . . Cover Letter Head. . . . . . . . . . . . . . . . 111 Newton’s lemma . . . . Ethical Dilemmas In Business. . . . . . . . . . . . . . . . . . . . . . . How Do You Do An Appendix In An. . . . . . . . . 115 Extensions of nonarchimedean valuations . . . . Ethical Essay. . . . . . . . You Do. . . . . . . . . . . 118.

Newton’s polygon . . . . . . . . . . . . . . . . . Dilemmas In Business Essay. . . . . . . . . . . . Resume Writing. . . . . . . 120 Locally compact fields . . . . . . . . . . . Ethical In Business. . . . . . . . . . . . . . . . . . Job Resume Ehow. . . . 122 Unramified extensions of ethical in business essay, a local field . . . . . . Head. . . . . . . . . . . . . . . . Dilemmas In Business. . . 123 Totally ramified extensions of K . . . . . . . . . . . . . . . . . . . . . Essays. . . . . . 125 Ramification groups . Dilemmas In Business Essay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Krasner’s lemma and applications . . . . . . . . You Do An Appendix In An. . Dilemmas Essay. . . . . . . . . . . . . . . . . 127 Exercises . . . . . . . . . . . . . . . . . Essays. . . . . . . . . . Ethical Dilemmas In Business Essay. . . . . . . . . . . . . 129. 8 Global Fields 131 Extending valuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 The product formula . . . . . . . . . . Essays. . . . . . . . . . Dilemmas In Business. . . . . . Contrasts. . . . . . . . . 133 Decomposition groups . . . . . . . . . . . . . . . . Dilemmas Essay. . . How Do Essay. . . . . . . Ethical Dilemmas Essay. . . . . . . . 135 The Frobenius element . . Job Resume Ehow. . . . . . . . . Ethical Essay. . . . . . . . . Writing. . . . In Business Essay. . . . . . . . . . . 137 Examples . . . . . . . . . . . . . Writing. . . Dilemmas Essay. . . . . . . . . Of Thunder. . . . . Ethical In Business. . . . . . . . . . . . 139 Computing Galois groups (the hard way) . . . . . . . . . Writing Verbs. . . . . . . . . . . . . . 140 Computing Galois groups (the easy way) . . . . . . . . . . . . . Dilemmas Essay. . Email Content. . . . . . . . . 141 Applications of the Chebotarev density theorem . . . . . . . . . . . Dilemmas Essay. . . . . . . Resume Verbs. . 146 Exercises . . . . . . . . . . . . . . . . . . . . Dilemmas In Business. . . . . . Essay On Roll Of Thunder Hear. . . . . . . . . . . . . . 147. A Solutions to the Exercises 149. B Two-hour examination 155. We use the standard (Bourbaki) notations: ND f0;1;2; : : :g; ZD ring of integers; RD field of real numbers; CD field of ethical dilemmas essay, complex numbers; Fp D Z=pZD field with p elements, p a prime number. For integers m and n, mjn means that m divides n, i.e., n 2mZ. Throughout the notes, p is a prime number, i.e., p D 2;3;5; : : :. Given an email content equivalence relation, ?? denotes the equivalence class containing . The empty set is denoted by ;. The cardinality of a set S is denoted by jS j (so jS j is the number of elements in S when S is finite). Let I and A be sets; a family of elements of A indexed by I , denoted .ai /i2I , is a function i 7! ai WI ! A. X Y X is a subset of Y (not necessarily proper); X. Ethical In Business Essay. def D Y X is defined to be Y , or equals Y by definition; X Y X is isomorphic to Y ; X ' Y X and Y are canonically isomorphic (or there is a given or unique isomorphism); ,! denotes an injective map; denotes a surjective map. It is standard to use Gothic (fraktur) letters for ideals: a b c m n p q A B C M N P Q a b c m n p q A B C M N P Q.

The algebra usually covered in a first-year graduate course, for example, Galois theory, group theory, and multilinear algebra. An undergraduate number theory course will also be helpful. In addition to the references listed at the end and in footnotes, I shall refer to the following of my course notes (available at how do you do in an essay, www.jmilne.org/math/): FT Fields and Galois Theory, v4.22, 2011. GT Group Theory, v3.11, 2011. Dilemmas Essay. CFT Class Field Theory, v4.01, 2011. I thank the following for providing corrections and comments for earlier versions of these notes: Vincenzo Acciaro; Michael Adler; Giedrius Alkauskas; Francesc Castella?; Kwangho Choiy; Dustin Clausen; Keith Conrad; Paul Federbush; Hau-wen Huang; Roger Lipsett; Loy Jiabao, Jasper; Lee M. Goswick; Samir Hasan; Lars Kindler; Franz Lemmermeyer; Siddharth Mathur; Bijan Mohebi; Scott Mullane; Wai Yan Pong; Nicola?s Sirolli; Thomas Stoll; Vishne Uzi; and resume verbs, others. PARI is an open source computer algebra system freely available from http://pari.math.u- bordeaux.fr/. FERMAT (1601–1665). Stated his last “theorem”, and dilemmas in business, proved it for mD 4. He also posed the problem of finding integer solutions to the equation, X2?AY 2 D 1; A 2 Z; (1) which is writing, essentially the problem1 of finding the units in Z? p A?.

The English mathemati- cians found an algorithm for solving the problem, but neglected to prove that the algorithm always works. EULER (1707–1783). He introduced analysis into the study of the prime numbers, and he discovered an early version of the quadratic reciprocity law. LAGRANGE (1736–1813). He found the complete form of the ethical essay quadratic reciprocity law: D .?1/.p?1/.q?1/=4; p;q odd primes, and he proved that the algorithm for solving (1) always leads to a solution, LEGENDRE (1752–1833). He introduced the “Legendre symbol” m p. , and job resume ehow, gave an incom- plete proof of the quadratic reciprocity law. He proved the following local-global principle for quadratic forms in three variables over Q: a quadratic form Q.X;Y;Z/ has a nontrivial zero in Q if and only if it has one in R and the congruence Q 0 mod pn has a nontrivial solution for all p and n. GAUSS (1777–1855). He found the first complete proofs of the quadratic reciprocity law. He studied the Gaussian integers Z?i ? in order to find a quartic reciprocity law. He studied the classification of binary quadratic forms over Z, which is closely related to the problem of finding the class numbers of quadratic fields.

DIRICHLET (1805–1859). In Business Essay. He introduced L-series, and used them to prove an analytic for- mula for contrasts, the class number and a density theorem for the primes in an arithmetic progression. Ethical. He proved the following “unit theorem”: let ? be a root of a monic irreducible polynomial f .X/ with integer coefficients; suppose that f .X/ has r real roots and 2s complex roots; then Z??? is a finitely generated group of rank rC s?1. KUMMER (1810–1893). He made a deep study of the arithmetic of cyclotomic fields, mo- tivated by a search for higher reciprocity laws, and showed that unique factorization could be recovered by the introduction of “ideal numbers”. He proved that Fermat’s last theorem holds for regular primes.

HERMITE (1822–1901). He made important contributions to quadratic forms, and he showed that the roots of a polynomial of degree 5 can be expressed in terms of elliptic functions. EISENSTEIN (1823–1852). He published the first complete proofs for the cubic and quartic reciprocity laws. Job Resume Ehow. KRONECKER (1823–1891). He developed an alternative to dilemmas in business, Dedekind’s ideals. Cover Head. He also had one of the most beautiful ideas in ethical in business mathematics for generating abelian extensions of number fields (the Kronecker liebster Jugendtraum).

RIEMANN (1826–1866). Studied the Riemann zeta function, and made the Riemann hy- pothesis. 1The Indian mathematician Bhaskara (12th century) knew general rules for finding solutions to the equa- tion. DEDEKIND (1831–1916). He laid the modern foundations of algebraic number theory by finding the correct definition of the ring of integers in a number field, by proving that ideals factor uniquely into products of prime ideals in such rings, and by showing that, modulo principal ideals, they fall into finitely many classes. Defined the zeta function of a number field. WEBER (1842–1913). Made important progress in class field theory and the Kronecker Jugendtraum. HENSEL (1861–1941).

He gave the job resume ehow first definition of the field of p-adic numbers (as the ethical in business essay set of infinite sums. n, an 2 f0;1; : : : ;p?1g). HILBERT (1862–1943). He wrote a very influential book on algebraic number theory in 1897, which gave the first systematic account of the theory. Some of his famous problems were on number theory, and have also been influential. TAKAGI (1875–1960). He proved the fundamental theorems of abelian class field theory, as conjectured by Weber and Hilbert. NOETHER (1882–1935). Together with Artin, she laid the foundations of modern algebra in which axioms and conceptual arguments are emphasized, and she contributed to the classification of central simple algebras over number fields. HECKE (1887–1947).

Introduced HeckeL-series generalizing both Dirichlet’sL-series and Dedekind’s zeta functions. ARTIN (1898–1962). He found the “Artin reciprocity law”, which is the main theorem of class field theory (improvement of Takagi’s results). Introduced the Artin L-series. HASSE (1898–1979).

He gave the first proof of local class field theory, proved the Hasse (local-global) principle for all quadratic forms over number fields, and contributed to the classification of central simple algebras over number fields. BRAUER (1901–1977). Defined the Brauer group, and contributed to the classification of central simple algebras over number fields. WEIL (1906–1998). Defined the Weil group, which enabled him to give a common gener- alization of Artin L-series and Hecke L-series. CHEVALLEY (1909–84). The main statements of job resume ehow, class field theory are purely algebraic, but all the earlier proofs used analysis; Chevalley gave a purely algebraic proof. With his introduction of ide?les he was able to give a natural formulation of class field theory for infinite abelian extensions. IWASAWA (1917–1998). He introduced an important new approach into algebraic number theory which was suggested by the theory of curves over finite fields.

TATE (1925– ). He proved new results in group cohomology, which allowed him to give an elegant reformulation of class field theory. In Business. With Lubin he found an explicit way of generating abelian extensions of local fields. LANGLANDS (1936– ). The Langlands program2 is a vast series of conjectures that, among other things, contains a nonabelian class field theory. 2Not to be confused with its geometric analogue, sometimes referred to as the geometric Langlands pro- gram, which appears to lack arithmetic significance. Introduction It is resume, greatly to be lamented that this virtue of the [rational integers], to be decomposable into prime factors, always the same ones for ethical dilemmas essay, a given number, does not also belong to the [integers of cyclotomic fields].

Kummer 1844 (as translated by Andre? Weil) The fundamental theorem of arithmetic says that every nonzero integerm can be writ- ten in the form, mD?p1 pn; pi a prime number, and that this factorization is essentially unique. Consider more generally an integral domain A. An element a 2A is said to essay questions hear, be a unit if. it has an inverse in A (element b such that ab D 1D ba). I write A for the multiplicative group of units in A. An element of A is said to prime if it is neither zero nor a unit, and dilemmas in business essay, if. If A is a principal ideal domain, then every nonzero element a of A can be written in the form, aD u1 n; u a unit; i a prime element; and this factorization is unique up to order and replacing each i with an associate, i.e., with its product with a unit. Our first task will be to discover to what extent unique factorization holds, or fails to hold, in how do you do in an essay number fields. Three problems present themselves.

First, factorization in a field only makes sense with respect to a subring, and so we must define the “ring of integers” OK in our number field K. Secondly, since unique factorization will fail in general, we shall need to find a way of measuring by how much it fails. Finally, since factorization is only considered up to units, in order to fully understand the arithmetic of K, we need to understand the dilemmas structure of the group of units UK in OK . THE RING OF INTEGERS. Let K be an algebraic number field. Each element ? of K satisfies an equation. ?nCa1? n?1 C Ca0 D 0. with coefficients a1; : : : ;an in Q, and ? is an cover head algebraic integer if it satisfies such an equation with coefficients a1; : : : ;an in Z. We shall see that the algebraic integers form a subring OK of K. The criterion as stated is difficult to apply. We shall show (2.11) that ? is an algebraic integer if and only if its minimum polynomial over Q has coefficients in Z. Consider for example the field K D Q? p d?, where d is a square-free integer. The. minimum polynomial of ? D aCb p d , b ¤ 0, a;b 2Q, is. In Business Essay. .X ? .aCb p d//.X ? .a?b. p d//DX2?2aXC .a2?b2d/; and writing verbs, so ? is an algebraic integer if and only if. 2a 2 Z; a2?b2d 2 Z: From this it follows easily that, when d 2;3 mod 4, ? is an dilemmas in business essay algebraic integer if and only if a and b are integers, i.e., and, when d 1 mod 4, ? is an algebraic integer if and verbs, only if a and b are either both integers or both half-integers, i.e., For example, the minimum polynomial of 1=2C p 5=2 is X2?X ?1, and so 1=2C. is an algebraic integer in Q? p 5?. Let d be a primitive d th root of 1, for example, d D exp.2i=d/, and letK DQ?d ?. Then we shall see (6.2) that. OK D Z?d ?D ?P.

as one would hope. A nonzero element of an integral domain A is said to be irreducible if it is not a unit, and can’t be written as a product of two nonunits. For example, a prime element is (obviously) irreducible. Ethical Dilemmas In Business Essay. A ring A is a unique factorization domain if every nonzero element of A can be expressed as a product of irreducible elements in essentially one way. Is the ring of integers OK a unique factorization domain?

No, not in general! We shall see that each element of OK can be written as a product of irreducible elements (this is true for hear, all Noetherian rings), and so it is the uniqueness that fails. Dilemmas In Business. For example, in Z? p ?5? we have. 6D 2 3D .1C p ?5/.1?. To see that 2, 3, 1C p ?5, 1?. p ?5 are irreducible, and essay of thunder hear my cry, no two are associates, we use the. p ?5 7! a2C5b2: This is multiplicative, and it is dilemmas, easy to see that, for ? 2OK , Nm.?/D 1 ” ? N? D 1 ” ? is a unit. (*) If 1C p ?5D ??, then Nm.??/D Nm.1C. p ?5/D 6. Thus Nm.?/D 1;2;3, or 6. In the. first case, ? is a unit, the second and third cases don’t occur, and in the fourth case ? is a unit. A similar argument shows that 2;3, and essay questions on roll my cry, 1?. p ?5 are irreducible. Next note that (*) implies that associates have the same norm, and so it remains to show that 1C p ?5 and.

1? p ?5 are not associates, but. has no solution with a;b 2 Z. Why does unique factorization fail in OK? The problem is that irreducible elements in. OK need not be prime. Ethical Dilemmas. In the above example, 1C p ?5 divides 2 3 but it divides neither 2. nor 3. In fact, in an integral domain in which factorizations exist (e.g. a Noetherian ring), factorization is unique if all irreducible elements are prime. What can we recover? Consider. Job Resume Ehow. 210D 6 35D 10 21: If we were naive, we might say this shows factorization is not unique in Z; instead, we recognize that there is a unique factorization underlying these two decompositions, namely, The idea of Kummer and Dedekind was to enlarge the set of “prime numbers” so that, for example, in ethical dilemmas in business Z? p ?5? there is a unique factorization, 6D .p1 p2/.p3 p4/D .p1 p3/.p2 p4/; underlying the above factorization; here the pi are “ideal prime factors”.

How do we define “ideal factors”? Clearly, an ideal factor should be characterized. by the algebraic integers it divides. Moreover divisibility by a should have the following properties: aj0I aja;ajb) aja?bI aja) ajab for all b 2OK : If in addition division by a has the how do you do in an essay property that. ajab) aja or ajb; then we call a a “prime ideal factor”. Since all we know about an ideal factor is the set of elements it divides, we may as well identify it with this set. Thus an ideal factor a is a set of elements of dilemmas in business, OK such that. 0 2 aI a;b 2 a) a?b 2 aI a 2 a) ab 2 a for all b 2OK I. it is prime if an addition, ab 2 a) a 2 a or b 2 a: Many of you will recognize that an ideal factor is what we now call an ideal, and a prime ideal factor is a prime ideal. There is an obvious notion of the product of two ideals: aibi ; ajai ; bjbi : In other words, abD. nX aibi j ai 2 a; bi 2 b. One see easily that this is again an ideal, and that if. aD .a1; . ;am/ and bD .b1; . ;bn/ then a bD .a1b1; . ;aibj ; . ;ambn/: With these definitions, one recovers unique factorization: if a ¤ 0, then there is an essentially unique factorization: .a/D p1 pn with each pi a prime ideal. Content. In the above example, .6/D .2;1C p ?5/.2;1?.

In fact, I claim. .2;1C p ?5/.2;1?. .3;1C p ?5/.3;1?. Dilemmas. .2;1? p ?5/.3;1?. For example, .2;1C p ?5/.2;1?. p ?5;6/. Since every gen- erator is divisible by 2, we see that. .2;1C p ?5/.2;1?. Conversely, 2D 6?4 2 .4;2C2. and so .2;1C p ?5/.2;1?. p ?5/ D .2/, as claimed. I further claim that the four ideals. .2;1C p ?5/, .2;1?. p ?5/, and .3;1?. p ?5/ are all prime.

For example, the obvious map Z! Z? p ?5?=.3;1?. p ?5/ is surjective with kernel .3/, and so. Z? p ?5?=.3;1?. which is an integral domain. How far is this from what we want, namely, unique factorization of elements? In other. words, how many “ideal” elements have we had to add to our “real” elements to get unique factorization. In a certain sense, only a finite number: we shall see that there exists a finite set S of ideals such that every ideal is of the form a .a/ for some a 2 S and some a 2OK . Better, we shall construct a group I of “fractional” ideals in which the principal fractional ideals .a/, a 2K, form a subgroup P of finite index.

The index is called the resume content class number hK of K. We shall see that. hK D 1 ” OK is a principal ideal domain ” OK is a unique factorization domain. Unlike Z, OK can have infinitely many units. For example, .1C p 2/ is a unit of infinite. order in Z? p 2? W. p 2/m ¤ 1 if m¤ 0: In fact Z? p 2? D f?.1C. p 2/m jm 2 Zg, and so. Z? p 2? f?1gffree abelian group of rank 1g: In general, we shall show (unit theorem) that the roots of 1 in K form a finite group .K/, and that. OK .K/Z r (as an abelian group); moreover, we shall find r: One motivation for the development of algebraic number theory was the attempt to prove Fermat’s last “theorem”, i.e., when m 3, there are no integer solutions .x;y;z/ to ethical, the equation. with all of x;y;z nonzero. WhenmD 3, this can proved by the method of “infinite descent”, i.e., from one solution, you show that you can construct a smaller solution, which leads to a contradiction3. The proof makes use of the factorization. Y 3 DZ3?X3 D .Z?X/.Z2CXZCX2/; and it was recognized that a stumbling block to proving the theorem for larger m is that no such factorization exists into polynomials with integer coefficients of degree 2. This led people to look at more general factorizations. In a famous incident, the French mathematician Lame? gave a talk at the Paris Academy in 1847 in which he claimed to prove Fermat’s last theorem using the following ideas. Let p 2 be a prime, and suppose x, y, z are nonzero integers such that.

Write xp D zp?yp D. Y .z? iy/; 0 i p?1; D e2i=p: He then showed how to obtain a smaller solution to the equation, and hence a contradiction. Liouville immediately questioned a step in Lame?’s proof in which he assumed that, in order to show that each factor .z ? iy/ is job resume ehow, a pth power, it suffices to show that the factors are relatively prime in in business pairs and their product is contrasts, a pth power. In fact, Lame? couldn’t justify his step (Z?? is not always a principal ideal domain), and Fermat’s last theorem was not proved for almost 150 years. Dilemmas In Business. However, shortly after Lame?’s embarrassing lecture, Kummer used his results on job resume ehow the arithmetic of the fields Q?? to prove Fermat’s last theorem for all regular primes, i.e., for all primes p such that p does not divide the class number of Q?p?. Another application is to finding Galois groups. The splitting field of a polynomial f .X/ 2Q?X? is a Galois extension of Q. Essay. In a basic Galois theory course, we learn how to compute the Galois group only when the degree is very small. By using algebraic number theory one can write down an algorithm to do it for any degree. For applications of algebraic number theory to elliptic curves, see, for example, Milne 2006. Some comments on the literature. COMPUTATIONAL NUMBER THEORY.

Cohen 1993 and Pohst and Zassenhaus 1989 provide algorithms for most of the construc- tions we make in this course. The first assumes the reader knows number theory, whereas the job resume ehow second develops the whole subject algorithmically. Ethical In Business. Cohen’s book is the essay hear my cry more useful as a supplement to this course, but wasn’t available when these notes were first written. While the books are concerned with more-or-less practical algorithms for fields of small degree and small discriminant, Lenstra (1992) concentrates on finding “good” general algorithms. 3The simplest proof by infinite descent is that showing that p 2 is irrational. HISTORY OF ALGEBRAIC NUMBER THEORY.

Dedekind 1996, with its introduction by Stillwell, gives an excellent idea of how algebraic number theory developed. Edwards 1977 is a history of algebraic number theory, con- centrating on the efforts to prove Fermat’s last theorem. The notes in Narkiewicz 1990 document the origins of most significant results in algebraic number theory. Lemmermeyer 2009, which explains the origins of “ideal numbers”, and other writings by the same author, e.g., Lemmermeyer 2000, 2007. 0-1 Let d be a square-free integer. Complete the verification that the ring of integers in Q? p d? is as described. 0-2 Complete the verification that, in Z? p ?5?, .6/D .2;1C p ?5/.2;1?. is a factorization of .6/ into a product of prime ideals. Ethical. CHAPTER 1 Preliminaries from Commutative.

Many results that were first proved for rings of integers in number fields are true for more general commutative rings, and it is more natural to prove them in that context.1. How Do You Do An Appendix Essay. All rings will be commutative, and have an identity element (i.e., an element 1 such that 1a D a for all a 2 A), and a homomorphism of rings will map the identity element to the identity element. A ring B together with a homomorphism of rings A! B will be referred to as an A-algebra. We use this terminology mainly when A is a subring of B . In this case, for elements ?1; . ;?m of B , A??1; . ;?m? denotes the smallest subring of B containing A and the ?i . It consists of all polynomials in essay the ?i with coefficients in A, i.e., elements of the form X. ai1. im? i1 1 . ? im m ; ai1. im 2 A: We also refer to A??1; . ;?m? as the A-subalgebra of B generated by the ?i , and when B D A??1; . ;?m? we say that the ?i generate B as an cover head A-algebra. For elements a1;a2; : : : of ethical dilemmas, A, we let .a1;a2; : : :/ denote the smallest ideal containing the ai . It consists of finite sums. P ciai , ci 2 A, and it is called the ideal generated by. a1;a2; : : :. When a and b are ideals in A, we define. aCbD faCb j a 2 a, b 2 bg: It is again an ideal in A — in fact, it is the smallest ideal containing both a and b. If aD .a1; . ;am/ and bD .b1; . ;bn/, then aCbD .a1; . ;am;b1; . ;bn/: Given an ideal a in A, we can form the quotient ring A=a. Let f WA!

A=a be the homomorphism a 7! aCa; then b 7! f ?1.b/ defines a one-to-one correspondence between the ideals of A=a and the ideals of A containing a, and. 1See also the notes A Primer of Commutative Algebra available on my website. 1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. Essays. A proper ideal a of A is prime if ab 2 a) a or b 2 a. An ideal a is prime if and only if the quotient ring A=a is an integral domain. A nonzero element of A is said to in business essay, be prime if ./ is a prime ideal; equivalently, if jab) ja or jb. An ideal m in A is maximal if it is maximal among the proper ideals of A, i.e., if m¤A and there does not exist an ideal a ¤ A containing m but distinct from it. An ideal a is maximal if and only if A=a is a field. Every proper ideal a of A is contained in a maximal ideal — if A is Noetherian (see below) this is obvious; otherwise the proof requires Zorn’s lemma.

In particular, every nonunit in A is contained in a maximal ideal. There are the implications: A is cover letter head, a Euclidean domain) A is a principal ideal domain ) A is a unique factorization domain (see any good graduate algebra course). Ideals in dilemmas products of rings. PROPOSITION 1.1 Consider a product of rings AB . If a and b are ideals in A and B respectively, then ab is an ideal in AB , and every ideal in AB is of this form. The prime ideals of AB are the ideals of the form.

pB (p a prime ideal of A), Ap (p a prime ideal of B). Contrasts. PROOF. Let c be an ideal in AB , and let. aD fa 2 A j .a;0/ 2 cg; bD fb 2 B j .0;b/ 2 cg: Clearly a b c. Conversely, let .a;b/ 2 c. Then .a;0/ D .a;b/ .1;0/ 2 c and .0;b/ D .a;b/ .0;1/ 2 c, and so .a;b/ 2 ab: Recall that an ideal c C is prime if and only if C=c is an integral domain. The map. has kernel ab, and hence induces an isomorphism. Now use that a product of rings is an integral domain if and only if one ring is zero and the other is an integral domain. 2. REMARK 1.2 The lemma extends in an obvious way to dilemmas in business essay, a finite product of rings: the writing verbs ideals in A1 Am are of the form a1 am with ai an essay ideal in Ai ; moreover, a1 am is prime if and only if there is a j such that aj is a prime ideal in Aj and ai DAi for i ¤ j: A ring A is Noetherian if every ideal in A is finitely generated. PROPOSITION 1.3 The following conditions on job resume ehow a ring A are equivalent: (a) A is Noetherian. (b) Every ascending chain of ideals. eventually becomes constant, i.e., for some n, an D anC1 D . (c) Every nonempty set S of ideals in A has a maximal element, i.e., there exists an ideal in S not properly contained in any other ideal in S . PROOF. (a) (b): Let a D S. ai ; it is an ideal, and hence is finitely generated, say a D .a1; : : : ;ar/. For some n, an will contain all the ai , and so an D anC1 D D a. (b) (c): Let a1 2 S . If a1 is not a maximal element of S , then there exists an a2 2 S such that a1 a2. If a2 is not maximal, then there exists an a3 etc.. From (b) we know that this process will lead to a maximal element after only finitely many steps. (c) (a): Let a be an ideal in A, and let S be the set of finitely generated ideals contained in a. Then S is nonempty because it contains the zero ideal, and so it contains a maximal element, say, a0 D .a1; : : : ;ar/.

If a0 ¤ a, then there exists an element a 2 ar a0, and .a1; : : : ;ar ;a/ will be a finitely generated ideal in a properly containing a0. This contradicts the definition of a0. 2. A famous theorem of Hilbert states that k?X1; . ;Xn? is Noetherian. In practice, al- most all the rings that arise naturally in algebraic number theory or algebraic geometry are Noetherian, but not all rings are Noetherian. For example, the ring k?X1; : : : ;Xn; : : :? of polynomials in an infinite sequence of symbols is not Noetherian because the in business chain of ideals. never becomes constant. PROPOSITION 1.4 Every nonzero nonunit element of a Noetherian integral domain can be written as a product of writing, irreducible elements.

PROOF. We shall need to use that, for elements a and b of an integral domain A, .a/ .b/ ” bja, with equality if and only if b D aunit: The first assertion is obvious. For the second, note that if a D bc and b D ad then a D bc D adc, and so dc D 1. Hence both c and d are units. Suppose the statement of the proposition is false for a Noetherian integral domain A. Then there exists an element a 2 A which contradicts the statement and is such that .a/ is maximal among the ideals generated by such elements (here we use that A is essay, Noetherian). Since a can not be written as a product of irreducible elements, it is not itself irreducible, and so a D bc with b and c nonunits.

Clearly .b/ .a/, and the ideals can’t be equal for otherwise c would be a unit. From the maximality of .a/, we deduce that b can be written as a product of irreducible elements, and similarly for c. Thus a is a product of irreducible elements, and we have a contradiction. 2. REMARK 1.5 Note that the proposition fails for the ring O of all algebraic integers in the algebraic closure of Q in C, because, for example, we can keep in extracting square roots — an algebraic integer ? can not be an irreducible element of O because. p ? will also be. an algebraic integer and job resume ehow, ? D p ? p ?. Thus O is not Noetherian. 1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. Let A be a ring. An A-module M is said to be Noetherian if every submodule is finitely generated.

PROPOSITION 1.6 The following conditions on an A-module M are equivalent: (a) M is Noetherian; (b) every ascending chain of submodules eventually becomes constant; (c) every nonempty set of submodules in M has a maximal element. PROOF. Similar to the proof of Proposition 1.3. 2. PROPOSITION 1.7 Let M be an A-module, and let N be a submodule of M . If N and M=N are both Noetherian, then so also is M . PROOF. I claim that if M 0 M 00 are submodules of M such that M 0N DM 00N and M 0 and M 00 have the same image in M=N , then M 0 DM 00. Ethical Dilemmas In Business Essay. To see this, let x 2M 00; the second condition implies that there exists a y 2M 0 with the same image as x inM=N , i.e., such that x?y 2N . Then x?y 2M 00N M 0, and so x 2M 0. Now consider an ascending chain of submodules of M . If M=N is how do you do an appendix, Noetherian, the image of the chain in ethical dilemmas essay M=N becomes constant, and if N is Noetherian, the intersection of the chain with N becomes constant. Now the claim shows that the chain itself becomes constant. 2. PROPOSITION 1.8 Let A be a Noetherian ring.

Then every finitely generated A-module is Noetherian. Resume. PROOF. If M is generated by a single element, then M A=a for some ideal a in A, and the statement is obvious. We argue by induction on the minimum number n of generators ofM . SinceM contains a submoduleN generated by n?1 elements such that the quotient M=N is generated by a single element, the statement follows from (1.7). 2. A ring A is said to local if it has exactly one maximal ideal m. In this case, A D Arm (complement of m in A). LEMMA 1.9 (NAKAYAMA’S LEMMA) Let A be a local Noetherian ring, and let a be a proper ideal in A. Let M be a finitely generated A-module, and define. aM D f P aimi j ai 2 a; mi 2M g : (a) If aM DM , then M D 0: (b) If N is a submodule of M such that N CaM DM , then N DM: Rings of fractions. PROOF. (a) Suppose that aM D M but M ¤ 0. Choose a minimal set of generators fe1; : : : ; eng for M , n 1, and write. e1 D a1e1C Canen, ai 2 a: Then .1?a1/e1 D a2e2C Canen: As 1? a1 is not in m, it is a unit, and so fe2; . ; eng generates M , which contradicts our choice of fe1; : : : ; eng. (b) It suffices to show that a.M=N/DM=N for then (a) shows that M=N D 0. Con- sider mCN , m 2M . From the assumption, we can write. aimi , with ai 2 a, mi 2M: and so mCN 2 a.M=N/: 2. In Business Essay. The hypothesis that M be finitely generated in the lemma is essential. For example, if A is a local integral domain with maximal ideal m ¤ 0, then mM DM for any field M containing A but M ¤ 0. Rings of fractions.

Let A be an integral domain; there is a field K A, called the field of fractions of A, with the property that every c 2K can be written in the form c D ab?1 with a;b 2A and b ¤ 0. For example, Q is the field of fractions of Z, and k.X/ is the field of fractions of k?X?: Let A be an integral domain with field of fractions K. A subset S of A is said to be multiplicative if 0 … S , 1 2 S , and S is closed under multiplication. If S is a multiplicative subset, then we define. S?1AD fa=b 2K j b 2 Sg: It is obviously a subring of K: EXAMPLE 1.10 (a) Let t be a nonzero element of A; then. Job Resume Ehow. St def D f1,t ,t2. g. is ethical dilemmas in business, a multiplicative subset of A, and we (sometimes) write At for S?1t A. For example, if d is a nonzero integer, then2 Zd consists of those elements of Q whose denominator divides some power of d : Zd D fa=dn 2Q j a 2 Z, n 0g: (b) If p is a prime ideal, then SpDArp is a multiplicative set (if neither a nor b belongs to p, then ab does not belong to p/. We write Ap for S?1p A. For example, Z.p/ D fm=n 2Q j n is not divisible by pg:

2This notation conflicts with a later notation in contrasts essays which Zp denotes the ring of p-adic integers. 1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. PROPOSITION 1.11 Consider an integral domainA and ethical dilemmas in business, a multiplicative subset S ofA. For an ideal a of A, write ae for the ideal it generates in S?1A; for an ideal a of S?1A, write ac for aA. Then: ace D a for all ideals a of S?1A aec D a if a is a prime ideal of A disjoint from S: PROOF. Let a be an ideal in S?1A. Clearly .aA/e a because aA a and a is an ideal in S?1A. For the cover letter head reverse inclusion, let b 2 a. We can write it b D a=s with a 2 A, s 2 S . Then aD s .a=s/ 2 aA, and so a=s D .s .a=s//=s 2 .aA/e: Let p be a prime ideal disjoint from S . Clearly .S?1p/A p. For the reverse inclu- sion, let a=s 2 .S?1p/A, a 2 p, s 2 S . Consider the equation a. Ethical In Business Essay. s s D a 2 p. Both a=s. and s are in A, and so at least one of a=s or s is in p (because it is prime); but s … p (by assumption), and so a=s 2 p: 2. PROPOSITION 1.12 Let A be an integral domain, and let S be a multiplicative subset of A. The map p 7! pe defD p S?1A is a bijection from the set of prime ideals in A such that pS D? to the set of prime ideals in S?1A; the inverse map is p 7! pA. PROOF. It is easy to see that. p a prime ideal disjoint from S) pe is a prime ideal in S?1A, p a prime ideal in S?1A) pA is a prime ideal in A disjoint from S; and (1.11) shows that the two maps are inverse.

2. EXAMPLE 1.13 (a) If p is a prime ideal in how do essay A, then Ap is a local ring (because p contains every prime ideal disjoint from Sp). (b) We list the prime ideals in some rings: Note that in general, for t a nonzero element of an integral domain, fprime ideals of Atg $ fprime ideals of A not containing tg. fprime ideals of A=.t/g $ fprime ideals of A containing tg: The Chinese remainder theorem. Recall the classical form of the theorem: let d1; . ;dn be integers, relatively prime in pairs; then for any integers x1; . ;xn, the dilemmas essay congruences. The Chinese remainder theorem. have a simultaneous solution x 2 Z; moreover, if x is one solution, then the other solutions are the integers of the form xCmd with m 2 Z and d D. We want to translate this in terms of ideals. Integersm and n are relatively prime if and only if .m;n/D Z, i.e., if and verbs, only if .m/C .n/D Z. This suggests defining ideals a and b in a ring A to be relatively prime if aCbD A. If m1; . ;mk are integers, then T .mi / D .m/ where m is the least common multiple. of the mi . Thus T .mi / . Ethical Dilemmas. Q mi /, which equals. Q .mi /. If the mi are relatively prime in. pairs, then mD Q mi , and so we have. Q .mi /. Note that in general, a1 a2 an essay hear a1a2 . an; but the ethical in business essay two ideals need not be equal. These remarks suggest the following statement. THEOREM 1.14 Let a1; . ;an be ideals in a ring A, relatively prime in pairs. Then for any elements x1; . Email Content. ;xn of A, the congruences. have a simultaneous solution x 2 A; moreover, if x is one solution, then the other solutions are the elements of the form xC a with a 2. Q ai . In other words, the. natural maps give an exact sequence.

PROOF. Suppose first that n D 2. As a1C a2 D A, there are elements ai 2 ai such that a1Ca2 D 1. The element x D a1x2Ca2x1 has the required property. For each i we can find elements ai 2 a1 and dilemmas in business, bi 2 ai such that. ai Cbi D 1, all i 2: The product Q i2.ai Cbi /D 1, and lies in a1C. Q i2 ai , and so. We can now apply the theorem in the case nD 2 to obtain an element y1 of verbs, A such that. y1 1 mod a1; y1 0 mod Y. These conditions imply. Ethical Essay. y1 1 mod a1; y1 0 mod aj , all j 1: Similarly, there exist elements y2; . ;yn such that. yi 1 mod ai ; yi 0 mod aj for j ¤ i: The element x D P xiyi now satisfies the requirements. 1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. It remains to prove that T. ai . We have already noted that T. ai . First suppose that nD 2, and let a1Ca2 D 1, as before. For c 2 a1a2, we have. c D a1cCa2c 2 a1 a2. which proves that a1 a2 D a1a2.

We complete the proof by essay, induction. This allows us to assume that. T i2 ai . We showed above that a1 and. Q i2 ai are relatively. prime, and so a1 . The theorem extends to A-modules. Dilemmas In Business. THEOREM 1.15 Let a1; . ;an be ideals in A, relatively prime in pairs, and let M be an A-module. Resume Verbs. There is an dilemmas exact sequence: This can be proved in the same way as Theorem 1.14, but I prefer to use tensor products, which I now review. Review of tensor products. Essay Of Thunder Hear. Let M , N , and ethical dilemmas in business essay, P be A-modules. A mapping f WM N ! P is said to be A-bilinear if. f .mCm0;n/D f .m;n/Cf .m0;n/ f .m;nCn0/D f .m;n/Cf .m;n0/ f .am;n/D af .m;n/D f .m;an/ 9=; all a 2 A; m;m0 2M; n;n0 2N: i.e., if it is linear in each variable. A pair .Q;f / consisting of an A-module Q and an A-bilinear map f WM N !Q is writing verbs, called the tensor product of M and N if any other A- bilinear map f 0WM N ! P factors uniquely into f 0 D ? ?f with ?WQ!

P A-linear. The tensor product exists, and ethical essay, is unique (up to a unique isomorphism making the obvious diagram commute). We denote it by M ?AN , and contrasts essays, we write .m;n/ 7! m?n for f . The pair .M ?AN;.m;n/ 7!m?n/ is ethical essay, characterized by each of the how do an appendix following two conditions: (a) The mapM N !M ?AN is A-bilinear, and any other A-bilinear mapM N ! P is of the ethical essay form .m;n/ 7! ?.m?n/ for a unique A-linear map ?WM ?AN ! P ; thus. BilinA.M N;P /D HomA.M ?AN;P /: (b) TheA-moduleM?AN has as generators them?n,m2M , n2N , and as relations. 9=; all a 2 A; m;m0 2M; n;n0 2N: Tensor products commute with direct sums: there is a canonical isomorphism. Review of tensor products.

It follows that if M and letter, N are free A-modules3 with bases .ei / and .fj / respectively, then M ?AN is a free A-module with basis .ei ? fj /. In particular, if V and W are vector spaces over a field k of dimensions m and n respectively, then V ?kW is a vector space over k of dimension mn. Let ?WM !M 0 and ?WN !N 0 be A-linear maps. Then. .m;n/ 7! ?.m/??.n/WM N !M 0?AN 0. is A-bilinear, and therefore factors uniquely through M N !M ?AN . Thus there is a unique A-linear map ???WM ?AN !M 0?AN 0 such that. REMARK 1.16 The tensor product of two matrices regarded as linear maps is called their Kronecker product.4 If A is essay, mn (so a linear map kn! km) and B is email resume content, r s (so a linear map ks! kr ), then A?B is the mr ns matrix (linear map kns! kmr ) with. [email protected] a11B a1nB. : : : . am1B amnB. 1CA : LEMMA 1.17 If ?WM !M 0 and ?WN !N 0 are surjective, then so also is. ???WM ?AN !M 0 ?AN. PROOF. Recall that M 0?N 0 is generated as an A-module by the elements m0?n0, m0 2 M 0, n0 2 N 0. By assumption m0 D ?.m/ for some m 2M and n0 D ?.n/ for some n 2 N , and in business, som0?n0 D ?.m/??.n/D .???/.m?n/. Therefore the image of ??? contains a set of generators for you do in an essay, M 0?AN 0 and so it is equal to it.

2. One can also show that if M 0!M !M 00! 0. is exact, then so also is. M 0?AP !M ?AP !M 00 ?AP ! 0: For example, if we tensor the exact sequence. with M , we obtain an exact sequence. a?AM !M ! .A=a/?AM ! 0 (2) 3Let M be an A-module. Elements e1; : : : ; em form a basis for M if every element of ethical essay, M can be expressed uniquely as a linear combination of the ei ’s with coefficients in A. Then Am!M , .a1; : : : ;am/ 7! an isomorphism of resume verbs, A-modules, and M is said to be a free A-module of rank m. 4Kronecker products of matrices pre-date tensor products by about 70 years.

1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. The image of a?AM in M is. P aimi j ai 2 a, mi 2M g ; and so we obtain from the exact sequence (2) that. By way of contrast, ifM !N is injective, thenM ?AP !N ?AP need not be injective. For example, take A D Z, and note that .Z. m ! Z/?Z .Z=mZ/ equals Z=mZ. which is the zero map. PROOF (OF THEOREM 1.15) Return to the situation of the theorem. When we tensor the isomorphism. with M , we get an isomorphism. M=aM ' .A=a/?AM ' ! Q .A=ai /?AM ' EXTENSION OF SCALARS.

If A! B is an A-algebra and M is an A-module, then B?AM has a natural structure of a B-module for which. b.b0?m/D bb0?m; b;b0 2 B; m 2M: We say that B?AM is the ethical in business B-module obtained from M by extension of scalars. The map m 7! 1?mWM ! B ?AM has the following universal property: it is A-linear, and for any A-linear map ?WM ! N from M into a B-module N , there is a unique B-linear map ?0WB?AM !N such that ?0.1?m/D ?.m/. Thus ? 7! ?0 defines an isomorphism. HomA.M;N /! HomB.B?AM;N/, N a B-module: For example, A?AM DM . If M is a free A-module with basis e1; : : : ; em, then B?AM is essays, a free B-module with basis 1? e1; : : : ;1? em. TENSOR PRODUCTS OF ALGEBRAS.

If f WA! B and gWA! C are A-algebras, then B ?A C has a natural structure of an A-algebra: the product structure is in business essay, determined by the rule. .b? c/.b0? c0/D bb0? cc0. and the map A! B?AC is a 7! f .a/?1D 1?g.a/. For example, there is a canonical isomorphism. a?f 7! af WK?k k?X1; : : : ;Xm?!K?X1; : : : ;Xm? (4) Review of tensor products. TENSOR PRODUCTS OF FIELDS. We are now able to compute K?k? if K is a finite separable field extension of a field k and ? is an arbitrary field extension of k. According to the primitive element theorem (FT 5.1), K D k??? for some ? 2K. Let f .X/ be the minimum polynomial of writing verbs, ?. Dilemmas In Business Essay. By definition this means that the map g.X/ 7! g.?/ determines an isomorphism.

Hence K?k? ' .k?X?=.f .X///?k? '??X?=.f .X// by (3) and head, (4). Because K is separable over k, f .X/ has distinct roots. Therefore f .X/ factors in ??X? into monic irreducible polynomials. that are relatively prime in pairs. We can apply the Chinese Remainder Theorem to deduce that. Finally, ??X?=.fi .X// is a finite separable field extension of ? of degree degfi . In Business Essay. Thus we have proved the you do an appendix essay following result: THEOREM 1.18 Let K be a finite separable field extension of k, and let ? be an arbitrary field extension. Ethical Dilemmas. Then K?k? is a product of finite separable field extensions of ?, If ? is a primitive element for K=k, then the image ?i of ? in ?i is a primitive element for?i=?, and questions of thunder, if f .X/ and fi .X/ are the minimum polynomials for ? and ?i respectively, then. EXAMPLE 1.19 Let K DQ??? with ? algebraic over in business Q. Then. C?QK ' C?Q .Q?X?=.f .X///' C?X?=..f .X//' Yr. iD1 C?X?=.X ??i / Cr : Here ?1; : : : ;?r are the conjugates of ? in C. The composite of in an, ? 7! 1??WK!

C?QK with projection onto the i th factor is. We note that it is essential to assume in (1.18) that K is separable over ethical dilemmas in business k. If not, there will be an ? 2K such that ?p 2 k but ? … k, and the ring K?kK will contain an element ? D .??1?1??/¤ 0 such that. ?p D ?p?1?1??p D ?p.1?1/??p.1?1/D 0: Hence K?kK contains a nonzero nilpotent element, and so it can’t be a product of fields. NOTES Ideals were introduced and studied by job resume ehow, Dedekind for rings of algebraic integers, and later by others in in business essay polynomial rings. It was not until the 1920s that the theory was placed in its most natural setting, that of arbitrary commutative rings (by Emil Artin and contrasts essays, Emmy Noether). Embed this document on your website. If you don't receive any email, please check your Junk Mail box.

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Essay on Homosexuality (2012) by D.J. Webb. Essay on Homosexuality. Published on the Libertarian Alliance Blog. Homosexuality is in many ways an awkward subject to write about.

In the old days, such things were not mentioned in polite conversation. Even today, the continual discussion of sexual orientation can grate: surely such things are meant to be intimate and private? However, conservatives do not set the essay, tone of public debate, and for good or ill homosexuality has become a high-profile topic of political discussion. First of email content all, it is worth pointing out that homosexuality has not been recently invented. There always have been men who were attracted to ethical essay other men. While strict homosexuality is found among a very small minority of the population, it is likely that the numbers of men who have been attracted to email some other men, or who have experimented along those lines, is dilemmas in business, much larger than the core homosexual demographic group. It is difficult to cite accurate figures, as not everyone is sure of his own sexuality, let alone confident in discussing it with researcher. The Kinsey Report compiled in 1948, entitled “Sexual Behaviour in the Human Male”, claimed that 46% of the men interviewed reacted sexually to another male at some point in their lives (the methodology that informed the report, including the selection of the pool of interviewees, has been questioned by some). Yet a government survey in the UK in 2010 put the “gay” section of the population at just 1.5%. This is a long way from being the statistical norm, leading some conservatives to contrasts essays conclude that “abnormality” makes homosexuality a “perversion” or even an in business illness, but the American Psychiatric Association declassified homosexuality as a mental disorder in 1973.

From a strictly psychiatric point of writing verbs view, a phenomenon often combined with high intellectual ability and ethical dilemmas in business, otherwise normal functioning in society should not be regarded as a mental disorder. Furthermore, it is fair to essay questions of thunder say that homosexuality is so widely found in human societies and across the ethical dilemmas in business essay, ages that, while not being the statistical norm, it must be described as a natural phenomenon. Societies need to how do an appendix in an essay be reproduced, and ethical dilemmas in business essay, should not be based purely around sexual urges, and so homosexuality cannot be thought of as a potential building block of society, but homosexuality is a human foible that will always exist in cover head society. It is an dilemmas essay interesting question whether a more open social attitude towards homosexuality will lead to its greater prevalence, as people who would otherwise repress their urges do not feel the need to do so. The reason why some menand homosexuality seems to be much more prevalent among men than womenare attracted to other men is ultimately unclear.

The “gay” movement seems to have adopted the line that it must be genetic, backed up by somewhat bizarre arguments about occasional homosexual behaviour among animals. But in fact no one really knows: it is as likely as not that current social policies that encourage marital breakdown lead to confused sexuality among boys, brought up without father figures. Some combination of reasons could also be in play, not least because some men have gone “gay” in later life, raising questions over how stable sexuality is throughout one’s life. The Christian church has long railed against homosexuality, whilst being a notable organisation in resume content which homosexual activity has always flourished. Before the Christian church embedded itself into in business essay the culture of Western Europe, homosexual behaviour was much more widespread in ancient Rome and ancient Greece, tending to show that genetic factors are not the key to understanding homosexuality, and contrasts, that social and in business, cultural factors are the main drivers of human sexuality. Email Content! I tend to believe that the genetic instinct gives us the sexual urge, without specifying in detail the ethical essay, kinds of human beings that are to be regarded as sexually attractive.

Of course, referring to homosexuality as a cultural phenomenon fits easily into the prevailing left-wing narrative concerning “cultural diversity”, which attempts to unpick the social and cultural norms of verbs Western society to justify multi-culturalism, apparently with the aim of ethical creating a society of people who no longer have cultural connections with each other, but are in the main clients of the state. If the way things have been done for centuries in the West has not always been the way, or is not the way in all societies, it is argued that our culture is worthless, or its worth is ultimately subjective, and so the how do you do in an, norms of society should be shunted aside in favour of a more generous, “liberal” approach. There are many ramifications of this, but I wish to stick to theme of ethical homosexuality here. Greek and Roman homosexuality appear to have been connected to the warrior culture: homosexual attraction was not seen as unmanly. It would be incorrect to impose modern notions of “gay identity” on the ancient world.

There was no gay identity, and it is interesting to cover head see that the main form that homosexual relations took in ancient Greece was of relations between an older warrior and a adolescent of 12-17 years of age. Ethical! Such relationships between people of different age groups are not really the intention of modern laws decriminalising homosexuality, where adolescents under 16 years of age are not seen as capable of giving consent to sexual activity (despite being almost universally engaged in it). Clearly, relationships between men and older youths in ancient Greece were not unmanly; neither did they detract in job resume ehow any way from masculinity. Ethical! There was nothing “camp” or “queenie” about Greek homosexuality. But if it was possible for one society to interpret human sexuality in a radically different way from the present, then couldn’t one argue that all cultural norms are essentially arbitrary? There is on roll of thunder hear my cry, a problem for conservatives here, in that England was traditionally a free country in most respects, and so we generally call for a restoration of our traditional cultural norms, and yet it is undeniable that the Christian narrative on sexuality had a deep impact on English culture. One could argue, however, that despite the mainstream nature of heterosexuality throughout English history, some degree of ethical dilemmas in business essay homosexuality was part of the social norm.

There always has been an undercurrent of homosexuality, and any attempt, legally, to create a society where all men adhered to heterosexual norms would in itself be a rejection of the realities of traditional England. Quite apart from homosexual attractions in the upper echelons of essays society (Richard the Lionheart, Edward II and James I spring to mind), there has for centuries been widespread practice of homosexuality among public schoolboys. Maybe this is why Roger Scruton in his England: An Elegy spoke of the ethical dilemmas essay, homosexual nature of English culture. It would be a gross misunderstanding to state that homosexuality has always been accepted, but England would not have been England without its undercurrent of relationships or sexual activity between men. Given that the Christian church is widely seen, even by its supporters, to have erred in many of the details of its teachings (e.g., on the Creation), I am wondering whether an contrasts essays English traditionalist approach could be devised that accepted the niche role of the dilemmas in business essay, church, and its architecture, liturgy and music, as a valued part of resume writing verbs our culture, while also seeing that prohibitions against harmless private behaviour need to dilemmas essay be downplayed, especially where state sanctions are involved. Whatever eventually emerges from questions on roll of thunder hear, genetic search on the reasons for homosexuality and whatever the rights and wrongs of church teaching on the subject, libertarians could not support the criminalisation of homosexual acts, giving the dilemmas, state, as it would, the right to resume investigate what is ethical, going on in private bedrooms and behind closed doors.

Laws against “sodomy” were repealed in 1967 in the case of participants over the age of 21, with the age of consent reduced in 2001 to 16. As far as I am concerned, this gives homosexualsand libertarians objecting to the criminalisation of sex between mennearly everything they want, albeit with a continuing question over resume, the absurd classification of sexual acts with consenting 15-year-olds as “statutory rape”. Another question that libertarians could take a stance on is laws against “public indecency” in ethical dilemmas essay gay cruising grounds, such as Hampstead Heath in you do London. Dilemmas! In George Orwell’s 1984 , Winston Smith was able to escape the eyes of Big Brother by having sex in job resume ehow the woods, and in any free society, unless the state proposed to place cameras on the branches of every tree, sex in essay the woods is simply something that is going to happen. Resume Writing Verbs! It is not necessarily something a cultured person would engage in, but we are talking about the laws of a free country here. Dilemmas In Business Essay! Sex behind bushes in known gay cruising grounds is not at all the same thing as similar behaviour out in the open in a way that would offend most people. It is interesting to note that England did not always have laws against homosexual acts. Before the 1533 Buggery Act, which criminalised anal sex, but not all homosexual acts, and specified hanging as the punishment, cases of “buggery”as it was charmingly knownwere handled by the ecclesiastical courts, with little evidence of any serious attempt to stamp out homosexual acts.

Of course, in mediaeval times, people depended on their children in older age, and in a largely agrarian society without pensions and other modern financial instruments, homosexuality as a public lifestyle, in resume content contradistinction to furtive acts conducted by people who otherwise adhered to ethical essay the general norms of family life, was unthinkable. The number of people put to death for buggery was necessarily small, as evidence would generally have been lacking. Verbs! The death penalty for buggery was abolished in 1861, and an 1885 Act of Parliament extended the sanction of imprisonment to ethical essay all homosexual activity between men and not just sodomy. Not all English conservatives seem to realise that homosexual acts (the broader definition thereof) were only illegal for 82 years, and so there is resume writing, nothing really traditionalist about regretting the demise of the 1885 Act. It is sometimes claimed that one cannot be a libertarian without supporting homosexuality. Is that really so? I don’t think one can be libertarian without opposing the ethical in business essay, criminalisation of homosexuality, but that is another thing entirely. Surely libertarians should oppose attempts to criminalise homosexuality and vocal opposition to homosexuality in equal measure. The right of others to deprecate homosexuality was mentioned during the Parliamentary debate on decriminalisation of content homosexuality in 1967, where the Earl of Arran, a sponsor of the bill, said.

I ask those who have, as it were, been in bondage and for whom the ethical dilemmas in business essay, prison doors are now open to show their thanks by comporting themselves quietly and with dignity. This is no occasion for jubilation; certainly not for email content celebration. In Business Essay! Any form of ostentatious behaviour; now or in the future any form of public flaunting, would be utterly distasteful and would, I believe, make the sponsors of the Bill regret that they have done what they have done. Of Thunder Hear My Cry! Homosexuals must continue to remember that while there may be nothing bad in being a homosexual, there is certainly nothing good. Lest the in business essay, opponents of the Bill think that a new freedom, a new privileged class, has been created, let me remind them that no amount of legislation will prevent homosexuals from being the subject of dislike and derision, or at best of pity. We shall always, I fear, resent the odd man out. That is their burden for all time, and they must shoulder it like menfor men they are. [ Hansard , 21 July 1967 ] Adoption and civil partnerships. Decriminalisation did not mean that homosexuality was to be promoted in all arenas of life, much less than opposition to homosexuality was to be criminalised. Yet the gay agenda has developed along more or less extreme lines that Lord Arran indicated would have made the sponsors of the email, 1967 Bill regret their actions. Not only can homosexual couplesor, worse, lone homosexual individualsadopt children today, opposition to such adoptions from the ethical in business essay, biological parents of children who have been taken into care is also ignored.

Civil partnerships were a further development that seemed to chip away at social norms, and now the government is talking about introducing “gay marriage”, as if marriage were not originally a religious concept in the first place. Much of this appears to many to be intent on creating a minority of people privileged by the state by dint of job resume ehow their statistically deviant behaviour. How should libertarians view these matters? As far as the adoption of children is concerned, the forgotten subjects of state intervention are the children. There is little evidence that raising children in novel and essay, innovative household units is how do you do in an, good for them: I am not denying that where one parent dies, the ethical, surviving spouse often remains a good parent.

But to go out of email resume our way to create family units where adopted children have a lone parent seems quixotic in terms of public policy. Given that men and women are different, and fathers and mothers bring something different to dilemmas the family and the child-rearing process, I pity the child who is job resume ehow, adopted by order of the state by two men or two women, simply to make a political point. Many of these children will grow up with no ill effects, but it seems more sensible to give all adopted children the natural family environment of ethical in business a father and a mother. There is nothing libertarian about extremist policies to the contrary. As far as civil partnerships are concerned, it is cover head, argued that taxation and inheritance systems treat married couples differently from single people, and essay, so men in long-term relationships need ways of avoiding being treated as single people. I think libertarians can be sympathetic to the idea that any committed peopleincluding two sisters and communes of many individualsshould be able to essays register as “fiscal units”, although our main approach is to eliminate personal taxation, which resolves most questions of this type. Consequently, the civil partnership arrangement should stay, although “ceremonies” organised by ethical essay, the state that appear to mimic marriage should end: civil partnership should be a simple application form in email resume content the post, and if the dilemmas, individuals concerned wish to have a party, then it would be up to contrasts them to ethical dilemmas in business organise it. The problem is partly the state’s view of marriage. Once marriage was taken out of the hands of the church and contrasts essays, made a preserve of the statewhich is what civil marriages in registry offices amount toarguably, heterosexual marriage was downgraded to the status now occupied by ethical dilemmas essay, civil partnerships. For marriage is resume verbs, not about becoming a “fiscal unit” for the purposes of state revenue collection; in Christian theology, a man and a woman become “one flesh”.

Although not originally related to each other, matrimony makes them one flesh, relatives of in business essay each other, a suitable state in cover letter which to approach the bearing of ethical dilemmas children. Two men cannot become “one flesh” in this way, precisely because they cannot have children together. Similarly, marriage is a vow in the sight of God. Whatever one’s views on the existence of God or otherwise, the on roll of thunder my cry, nature of a vow is that it cannot be revoked, whether by the church or by the state. A solemn vow binds the individual for life (and I include here the in business, Coronation Oath and judicial and political oaths of office). To claim that the state can “divorce” a couple makes a mockery of the vow, and means the couple were not really “one flesh” all along: civil marriage is therefore just civil partnership. The reason why I oppose “gay marriage” is that the state cannot make anyone “one flesh”. It is a detail of Christian theology that the sacrament of matrimony does accomplish this in the case of a man and a woman, and this theology is backed up by the biological reality that a man and a woman do become related to each other (“one flesh”) by their joint relationship to and through their children. Even if the state hands out certificates saying two men are “married”, they cannot be married, any more than UK passports handed out to letter head Africans make them truly British. I would like to abolish divorce too and essay, go for a dual-track approach: if you wish to get married in church, to take solemn vows, which may or may not mean anything to any Supreme Being that may exist, then the state cannot declare those vows defunct; but if you wish merely to get married “in the eyes of the state”, then a man and woman should be able to send a civil partnership application form to the government in the way I outlined above or enter a civil partnership at a registry office, in the same way that two men can.

Such civil partnerships should not contain solemn vows, and could therefore be dissolved by questions, the state. I will later in this article argue, however, that libertarians should not officially take a position against gay marriage for dilemmas in business essay tactical reasons. One area where libertarians must take a clear view is the contrasts essays, use of in business state power to crush opposition to homosexuality, which seems many times more determined than the rare use of the law against homosexual acts before 1967. People must be free to express their views on homosexuality. Yet the spread of notions of political correctness appears to turn people into email content “tolerance machines”, people whose views have all been decided for ethical dilemmas in business them by the state, and cover head, who have no business other than to repeat the views intoned in the media and the education system. For this reason, I am reluctant to say that libertarians “should” feel favourably or unfavourably disposed to ethical essay homosexuality.

People, including libertarians, who are instinctively averse to homosexuality, as I am to on roll lesbianism, should feel no compunction about saying so, although, as stated above, support for state sanctions for homosexuality is another issue entirely, well beyond any reasonable turf for any real libertarian. All laws designed to “enforce” acceptance of homosexuality should be abolished. Not only do people have to be careful at work nowadays how they express themselves on the subjectthe authorities are only too eager to destroy the careers of those who step out of linelaws against freedom of association are also being used to crush dissent. In 2011, two gay men won £3,600 in damages after being turned away from ethical, a bed and breakfast guesthouse in Cornwall and a number of an appendix similar cases have come to light . Such “discrimination” is illegal, and it seems gay men have a licence to cash in where they know the owners of a BB are Christians. Anti-discrimination laws are a fundamental plank in a coercive approach to ethical in business essay creating a multi-cultural society. Job Resume Ehow! Nevertheless, particularly in the case of family-run businesses, the owners have the rightthe moral right, not the legal rightto offer their services to customers on whatever basis they choose. Essay! It is undoubtedly more than a little petty for BB owners to lay down rules on who can sleep in double beds, but their religious or political beliefs may be strongly held, and it is not for anyone else to tell them they may not act upon them. In the case of large hotels or other non-family-run businesses, I think the principle still applies, that the you do an appendix, owners of the business have the right to specify who they will serve.

But in the case of essay large companies, it should be the shareholders, at an annual general meeting, who decide, and contrasts, not some little Hitler of a manager who doesn’t even own the company. I think it highly unlikely the shareholders of any company would demand discriminatory policies, as companies have an interest in expanding their customer bases, and so the issue only really crops up with small family-run businesses, giving the lie to dilemmas the claim that laws against discrimination are required to enable gay men and other favoured minorities to function in society. Finally, equality before the law should be re-established. This means that laws labelling certain crimes as “hate crimes” and imposing stiffer penalties on them should be abolished. This is not the same thing as supporting hate crimesI don’t support thembut surely it makes sense for the law to criminalise assault and battery of all members of society to an equal degree, without distinction. An interesting question is homosexuality in the armed forces. As male-dominated organisations, the armed forces are, like the church, a historic focus of homosexual employment. How Do You Do An Appendix Essay! Homosexual activity between sailors is nothing new. Dilemmas In Business! What should the official policy on homosexual employment in the armed forces be? Firstly, I think it important to state that, in you do in an extreme situations, such as wartime, all members of society have to be prepared to defend that society. Ethical Dilemmas In Business! That is what membership of letter society means.

Maybe some libertarians would claim that conscription should not be implemented in a free society. However, by the time war breaks out, social freedoms are the ethical dilemmas, last thing on the government’s mind. Warfare, especially when the nation is under attack, and not attacking other countries, is an extreme event, and many of the social niceties disappear overnight. Consequently, I am opposed to job resume ehow allowing conscientious objectors to absent themselves from the armed forces while others are being conscripted. But, by ethical dilemmas, the same token, homosexuality cannot be a sufficient reason to avoid the cover letter head, draft either. It is absurd for any society to hold that gay man cannot fight for dilemmas essay the country: in wartime, there may be little choice.

However, I see no reason why military discipline should not require decorum of members of the email resume content, armed forces, and ethical essay, “camp” behaviour or constant ribald discussion of gay sex in army barracks in a way likely to give rise to offence, should be deemed to contravene military discipline. Army officers should be in a position to insist that public decency is questions of thunder hear my cry, maintained at dilemmas in business, all times and that the issue doesn’t become a cause for strife between soldiers. I will address ecclesiastical homosexuality in passing here. How Do Essay! As the dilemmas, church, if it is to be a church, and not just a conveyor belt for political propaganda, has to be faithful to its teachings dating back millennia, I see no why priests should publicly proclaim their homosexuality without being defrockedif they are gay, why are they trying to verbs subvert the church by joining it in order to flout its commands? The preaching of homosexual rights from the pulpit should lead to the rapid defenestration of the vicar. Nonetheless, a realistic acceptance that many priests are gay is ethical, appropriate in the context where many of the how do you do essay, church’s teachings are no longer sustainable as historic or scientific truth. This means we shouldn’t poke around in a vicar’s private life to find out ethical in business essay if he is email resume content, gay, and if it becomes known that he is essay, gay without his seeking to how do you do in an flaunt himself, then a logical approach would be to ignore it. As with the armed forces, if public decorum is maintained, there is little reason to launch witch-hunts.

Interestingly, as sexuality becomes politicised, it has also become more fluid. The women of England seem to be getting less feminine as the men of England become less masculine. One example of ethical dilemmas this is the email content, metrosexual phenomenon, of which the football player, David Beckham, is in business, one example. Young “straight” men today worry about their appearance more than before, have more creams and potions in on roll of thunder their bathroom cabinets, and even engage in ethical dilemmas in business what I regard as the unmanly habit of shaving their body hair. When I was a teenager, such things would have been seen as effeminate. Looking around my local gym, it is clear that many of the younger men are rather feminine, or even effeminate, in appearance.

The days when heterosexuality meant raw masculinity are long gone. Essay Questions Hear My Cry! One could argue that a supine population that allows the in business, state to determine their views on race, culture and job resume ehow, sexuality is less manly that what went before. Ethical Essay! For this reason alone, I think libertarians could lament the decline of masculinity. Would “real men” have allowed their primary-school-age children to be bombarded with propaganda on anal sex? Intriguingly, and verbs, with an dilemmas essay eye on ancient Greece where homosexual relationships were not seen as diminishing one’s masculinity, this opens up the prospect of resume a redefinition of masculinity. If many of the “straight” lads are a good deal more effeminate than some of the gay men, then who are the real pansies? It was while I was thinking along these lines that I came across Jack Donovan’s website , where his books on “androphilia” and masculinity are listed. Apparently, Jack Donovan is an American androphilea man who likes menwho does not identify with the “gay” culture. The “gay” word is problematic for me, as it is politically loaded as an earlier attempt to “rebrand” homosexuality, and the gay culture that has been created around it seems to categorise gay men as soft, soppy, sissyish, something that homosexual acts were not associated with in ancient Greece. But a glance at the gay club scene also turns up dungeons, leather and chains, and one could also question whether anal sex (not the only form of gay sex, it should be added) is really sissyish at all: arguably, it is sex at its most primeval, sex in the animal sense; not really effeminate at all. Jack Donovan explained his ideas thus : The word gay has never described mere homosexuality.

Gay is a subculture, a slur, a set of dilemmas in business gestures, a slang, a look, a posture, a parade, a rainbow flag, a film genre, a taste in music, a hairstyle, a marketing demographic, a bumper sticker, a political agenda and philosophical viewpoint. Gay is a pre-packaged, superficial personaa lifestyle. It’s a sexual identity that has almost nothing to do with sexuality. Job Resume Ehow! Androphilia is a rejection of the overloaded gay identity and a return to a discussion of homosexuality in ethical dilemmas in business essay terms of desire. The gay sensibility is a near-oblivious embrace of a castrating slur, the non-stop celebration of an age-old, emasculating stigma applied to men who engaged in homosexual acts. Resume! Gays and radical queers imagine that they challenge the status quo, but in appropriating the stigma of effeminacy, they merely conform to and confirm long-established expectations. Homosexual men have been paradoxically cast as the enemies of masculinityslaves to in business the feminist pipe dream of a ‘gender-neutral’ (read: anti-male, pro-female) world. Androphilia is a manifesto full of truly dangerous ideas: that men can have sex with men and cover head, retain their manhood, that homosexuality can be about ethical championing a masculine ideal rather than attacking it, and that the “oppressive construct of masculinity” despised by job resume ehow, the gay community could actually enrich and in business, improve the lives of homosexual and bisexual men.

Androphilia is for those men who never really bought what the how do, gay community was selling. It is a challenge to leave the gay world completely behind and to rejoin the ethical in business essay, world of essay questions hear men, unapologetically, as androphiles, but more importantly, as men. I don’t know how far Jack Donovan’s ideas on masculinity and ethical in business, androphilia will spread, but I think it is at resume verbs, least possible that the relationship between homosexuality and effeminacy (or, conversely, between heterosexuality and masculinity) is dilemmas in business, breaking down, and it would be interesting to see the outcome. As sexuality seems more fluidI could well believe that 46% of men have felt attraction to a man at essays, some point (the unattractiveness of the average British female may play a role in this)more young men may be interested in an androphile alternative than in becoming gay per se . And a resurgence of masculinity in ethical dilemmas in business society would be a good thing. Email Resume Content! I haven’t yet had chance to buy Donovan’s book, so I don’t know if AIDS is mentioned therein.

But I would argue that turning the gay “community” into a vehicle for AIDS propaganda and ethical dilemmas, the distribution of condoms represents part of the effeminate culture of gayness. Real sex, whether between men and women or between two men, is without intervention of rubber. Another point I don’t know whether Donovan makes is that in order to become masculine, gay men must stop sliding into verbs a kind of gingerbread group for political correctness. Real masculinity includes applauding the dilemmas, expression of questions on roll of thunder real views by real people. Calling on the state to solve your battles is ethical essay, unmanly, and it would tend to paint all gay men as a group of resume writing extremists lobbying for essay more intervention by the technocracy. In fact, prejudice against homosexuality would appear to job resume ehow be largely justified in England today on dilemmas in business essay, political grounds, given the email resume content, way that leading gay activists appear on our television screens calling for essay more laws against discrimination and for sterner punishment of dissenters. Libertarians may well feel inclined, if not to support criminalisation of homosexuality, then to see the official gay movement and its spokesmen are enemies of a free country. Yet, curiously, most gay men I have ever met have opposed gay marriage and the adoption of children by homosexuals. Jack Donovan has also spoken out against gay marriage in an interesting article on the Alternative Right website : Same-sex marriage, however good its proponents believe it might be for you do an appendix in an essay homosexuals, is essentially an ethical attempt to subvert the cultural primacy of the email resume, reproductive family. Gays will not allow themselves to consider the fact that this spells death for civilizations, and that society has a rational interest in promoting big, patriarchal families above all other arrangements.

The idea that somehow, without any cultural apparatus to encourage or foster it, men and women will naturally take on the burden of raising a large family at any cost is simply absurd and proven wrong by below-replacement-level birth rates in Europe. Cultures that don’t place the highest value on reproductive families die out, and their numbers are replaced by cultures that do. It’s happening in Europe, and it’s happening in the US. While alternative relationships need not be openly scorned, and they may deserve some sort of in business essay reasonable accommodation, it isn’t in job resume ehow the best interest of Western Civilizationor any civilizationto morally or institutionally equate reproductive and ethical in business, non-reproductive sexuality. Reproductive sexuality is an indispensable building block of civilization; it serves society as a whole. Non-reproductive sexuality is, in on roll my cry the big picture, basically a “feel-good”. There is ethical dilemmas, some truth in the idea that homosexuality was symptomatic of the downfall of ancient Rome. There is no direct connection between the two, but Romans lolling about in bath-houses engaged in sex were leading too soft a life, and essay questions hear, unsurprisingly fell at the hands of the barbarians. Ethical In Business Essay! Bread and circusesand sexcreated an image of debauchery that Christians have down the centuries condemned. Arguably, our societies today have fallen victim to the same effete, effeminate social trends.

Welfarism, family breakdown and divorce, the compensation culture and the sexualisation of mainstream culture all form part of our social decline and I don’t see how libertarianism can accomplish any of its goals by supporting these trends. These trends all lead to greater social intervention to repair the inevitable social problems thrown up. One could argue that homosexuality has degraded the wider culture, by creating the goal of no-strings-attached sex. Now nightclubs are full of men and women in their 30s and 40s trying to play the field still, where once they would have been looking after their children at home. Clearly, this is an option for gay men, with no children, but for writing verbs men and women with children to attempt to dilemmas in business essay behave in essay of thunder hear my cry the same libertine manner has many negative social consequences. I would respond by removing all government subsidies for family breakdown, including welfare for unmarried mothers.

If people have children, they must accept the responsibility that entails. However, just as Roman debauchery was only a problem in the closing days of the Empiresex between men was hardly the direct cause of the ethical in business essay, fall of the Empire, and job resume ehow, was at one point a factor in strengthening society by promoting relationships between older and younger members of the warrior classso it would be inaccurate to see homosexuality as always leading to the decline of a society. Ethical Dilemmas! Our societies are too soft. The decline of masculinity has many causes, but homosexuality per se is not emasculating. So libertarians should broadly support the right to gay sex, while focusing their condemnation on the illiberal attempts to close down dissent and enforce acceptance of homosexuality. I have made clear my distaste for gay marriage, and indeed my preference for abolition of divorce and other policies designed to prevent family breakdown. However, there is always a hierarchy of policies of greater or lesser importance to political movements, and job resume ehow, laws that impinge on 1.5% of the population, with the numbers taking up the chance to “marry” in registry offices likely to be only in the hundreds, need to be seen in perspective. In Business! Consequently, libertarians need to email resume adopt a strategic approach. The really big issue for in business essay libertarianism is the panoply of multi-culturalism that is the real driver behind the cover, loss of our freedoms. There is a distinct possibility that appearing obsessed on the gay issue would prevent a wider hearing for dilemmas essay our ideas on social freedom.

For this reason, while libertarians will have a range of opinions on letter, the subject of gay marriage, the libertarian movement itself should adopt a neutral stance on the issue. Oddly enough, just as many gays, feeling, as they are in many ways, like social outsiders, became a Trojan Horse for political correctness, there are a number of well-known homosexuals, including the British historian, David Starkey, who will push the boundaries of what can be said on ethical dilemmas, the race issue. Homosexuality, until the late 1980s at least, used to contrasts essays have a considerable aura of ethical in business daring about it, bringing down social taboos and transgressing social norms. The reinvention of homosexuality as just another strand of the state’s attempt to create a cowed population has taken the audaciousness out letter of the homosexual experience: is it any wonder that men who like men sometimes take the lead in a politically correct society by saying the unsayable in ethical in business other areas? Clearly people like David Starkey have something to contribute to the advance of the libertarian movement in the UK, and so the contours of masculinity and support for state intervention have become confused and could become even more so in the future. Let’s have fewer young men depilating their groins and putting gel on their hair, and more young men of all sexual orientations insisting on their right to say and think what they like. A free country would be a country for real men! By Keir Martland.

Conservative Party Politicians. Into the letter head, Cannibal's Pot: Lessons for dilemmas in business America from Post-Apartheid South Africa. The University Outside State Control. Arnold Harris Mathew and the Old Catholic Movement in England 1908-52. Joseph-Rene Vilatte (1854-1929): Some aspects of his life, work and succession. Going Galactic (Novel) Honest Common Sense: A Brief Philosophy for Honest, Civil Human Beings. Fiction by Sean Gabb. The Churchill Memorandum. The Column of Phocas. Non-fiction by how do essay, Sean Gabb.

Acts of the Apostles: A Greek, Latin and English Parallel Text, Being an Aid for in business Adults to the Easier Learning of the Classical Languages. Freedom of of thunder my cry Speech in England. Cultural Revolution, Culture War. Smoking, Class and the Legitimation of Power. War and the National Interest: Arguments for a British Foreign Policy.

Dispatches from a Dying Country. The Land Question in Classical Liberal Thought and the Georgist Contribution to ethical dilemmas Classical Liberalism: A Bibliography. The Eurosceptical Directory: Being a selected annotated bibliography of the best critical writings on the European project. Freedom, Healthcare and Welfare Policy: A Selected Bibliography: A Resource Guide for Policy Makers, Politicians, Researchers, Academics, Healthcare Workers and Businessmen. The Works of Arthur Seldon (1916-2005): A Bibliography. Novels by Richard Blake. (Coming again Soon!) Books Partly by Sean Gabb. Down with Power: Libertarian Policy in a Time of Crisis (L.

Neil Smith, Introduction by how do you do an appendix in an essay, Sean Gabb) Economy and Virtue. Truancy in English Secondary Schools. Don't Fence Me in: Essays on the Rational Truant.

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