Timeline for If a polynomial f is irreducible then (f) is radical, without unique factorization?
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2011 at 19:57 | vote | accept | aglearner | ||
| Mar 9, 2011 at 9:39 | answer | added | Hailong Dao | timeline score: 7 | |
| Mar 9, 2011 at 6:44 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Mar 9, 2011 at 6:41 | comment | added | Pete L. Clark | I agree with Qiaochu. We all prefer questions which are (in some sense which is hard to nail down but is something you learn during your mathematical training) "natural", indeed so strongly that we will instinctively try to perturb an unnatural question to get a natural one. If you are asking something which goes against the grain of "perceived naturality", by all means tell us why: to do otherwise is, from a purely cognitive perspective, an unnecessary waste of time. (By the way, "I hate the author of Y" does not seem to me to be a good reason to avoid Y in the proof of X.) | |
| Mar 8, 2011 at 19:18 | comment | added | Qiaochu Yuan | @darij: yes, but I would strongly prefer that the OP give at least one such reason. In this case I see no benefit in seeking an alternate proof and IMO the burden of proof is on the OP to suggest a reason to believe that there is one. | |
| Mar 8, 2011 at 18:59 | comment | added | darij grinberg | I am growing annoyed by the tendency to answer questions like "how to prove X with Y" with "why don't you like Y?". There can be lots of reasons for this, beginning with "the classical proof of Y is non-constructive", "the proof of Y does not generalize as far as I want to generalize X", "I hate the author of Y" or simply "I was not able to come up with a proof of Y on my own and now I have sworn never to use Y". This is all irrelevant. Mathematics has always profited from having various proofs for one and the same result. | |
| Mar 8, 2011 at 18:02 | answer | added | Pete L. Clark | timeline score: 9 | |
| Mar 8, 2011 at 12:59 | comment | added | Emerton | Dear agleaner, I strongly recommend proving the UFD property for polynomial rings. Remember that your undergraduates will have been factoring polynomials since they were 11 or 12 years old, so their intuition behind unique factorization should be pretty solid. Also, later on, if you want to discuss examples like hypersurfaces and so on, you will be rather hamstrung if you don't have the UFD property to help you. Regards, Matthew | |
| Mar 8, 2011 at 10:29 | comment | added | Qiaochu Yuan | If that was your motivation, you should have said something to that effect in your question. In any case, I feel like undergraduates ought to know that polynomial rings are UFDs anyway. | |
| Mar 8, 2011 at 10:19 | comment | added | aglearner | So sad... First time my question on mathoverflow is down-voted... It took me one month to absorb this UFD property, and when you teach algebraic geometry for undergraduates you try your best to simplify the course... This is the reason why I wanted to avoid proving UFD property. But, it start to seem that this will be hard indeed | |
| Mar 8, 2011 at 10:06 | comment | added | aglearner | I agree, this is a bit silly, not that UFD property is hard... but it takes two pages to prove, i.e., one more lecture to give... | |
| Mar 8, 2011 at 9:51 | answer | added | Qiaochu Yuan | timeline score: 8 | |
| Mar 8, 2011 at 9:40 | comment | added | Qiaochu Yuan | Why are you so intent on avoiding the fact that polynomial rings are UFDs? | |
| Mar 8, 2011 at 9:35 | history | asked | aglearner | CC BY-SA 2.5 |