Timeline for Properties of rings that have an elegant description in terms of the associated category of modules
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 4, 2014 at 19:18 | history | rollback | Steven Landsburg |
Rollback to Revision 1
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| Jul 4, 2014 at 19:18 | comment | added | Steven Landsburg | @EricWofsey : In view of your comment, I'm rolling back my edit. | |
| Jul 4, 2014 at 18:07 | comment | added | KConrad | @StevenLandsburg: Admittedly my whole comment was pedantic, so with that in mind I would not consider factoring ideals to be something that includes the zero ideal as an object of interest, e.g., in a Dedekind domain nobody ever considers a factorization of the zero ideal, but only factorization of nonzero ideals as products of nonzero prime ideals. You'd lose the uniqueness of prime ideals factorization in a Dedekind domain if you want to bring the zero ideal into consideration. | |
| Jul 4, 2014 at 15:46 | comment | added | Eric Wofsey | Surely the ideal $(1)$ can be considered as the empty product of primes. | |
| Jul 4, 2014 at 15:24 | comment | added | Steven Landsburg | @KConrad: I edited to insert the word "proper", which deals with $(1)$. It seems to me that $(0)$ is prime and therefore (trivially) a product of primes, so I'm not clear on why you say that's also problematic. | |
| Jul 4, 2014 at 15:22 | history | edited | Steven Landsburg | CC BY-SA 3.0 |
added 7 characters in body
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| Jul 4, 2014 at 3:48 | comment | added | KConrad | You want a constraint on the ideals. For a field, the module condition is automatically true while the condition on ideals is false for (0) and (1), the only ideals. | |
| S Jul 4, 2014 at 3:29 | history | answered | Steven Landsburg | CC BY-SA 3.0 | |
| S Jul 4, 2014 at 3:29 | history | made wiki | Post Made Community Wiki by Steven Landsburg |