Timeline for Commutative algebra final project
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 15, 2011 at 2:20 | comment | added | Paul Siegel | I am by no means a number theorist (or even an algebraist) and I don't think I've encountered the book of Samuel that you're referring to, so I'll defer to your judgement here. I brought up the example because it was particularly formative in my own experience with commutative algebra. I first started learning about algebraic number theory a bit after I had already taken a course on commutative algebra, and I vividly remember how a lot of the abstract machinery that had confused me the first time around finally "clicked" when I saw the proof that primes split in a finite algebraic extension. | |
| Sep 14, 2011 at 22:36 | comment | added | Wanderer | I agree that it's a bit dangerous, and moreover some of the students will be following a parallel class on algebraic number theory or algebraic geometry - even though they won't be doing schemes, so I'd have to think about it some more. | |
| Sep 14, 2011 at 21:03 | comment | added | Pete L. Clark | @Mariano: well, sure. It's just that (in particular) Samuel lays things out so nicely that this is more of a reading project than a writing project. | |
| Sep 14, 2011 at 20:51 | comment | added | Mariano Suárez-Álvarez | Wouldn't having read Samuel's little book itself be a great thing to come out with from the project? | |
| Sep 14, 2011 at 20:01 | comment | added | Pete L. Clark | @Paul: perhaps predictably, as an algebraic number theorist I worry that your second proposal is a little too "pat". There are plenty of texts which lead you by the hand from scratch to the factorization of ideals into primes in any Dedekind domain (and also prove that the integral closure of a Dedekind domain in a finite separable field extension is a Dedekind domain, so $\mathbb{Z}_K$ is one). If you don't have any background here, this could be 15-20 hours of work, but there's little or no synthesis required: e.g. copying out relevant passages from Samuel's little book would suffice... | |
| Sep 14, 2011 at 19:04 | history | answered | Paul Siegel | CC BY-SA 3.0 |