Timeline for Why is it a good idea to study a ring by studying its modules?
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| Mar 29, 2011 at 3:00 | comment | added | Jose Brox | This is what is usually called 'the homological study' of ring theory | |
| Mar 28, 2011 at 23:59 | comment | added | Pete L. Clark | @Greg: +1. Indeed my own commutative algebra notes (as well as the class currently being taught out of them) take this perspective a lot. For instance, just today I proved that for a commutative ring $R$, all modules are projective iff $R$ is a finite direct product of fields. To my taste, a lot of the standard texts don't emphasize these sort of "inverse problems" as much as they should (e.g. where is this fact in Atiyah-Macdonald or Matsumura? perhaps some exercise, but I don't know where). | |
| Mar 28, 2011 at 19:10 | history | answered | Greg Marks | CC BY-SA 2.5 |