Timeline for Why is it a good idea to study a ring by studying its modules?
Current License: CC BY-SA 2.5
6 events
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| Dec 5, 2009 at 4:48 | comment | added | user709 | @Konrad: I dont' think you have addressed Qiaochu's question. I guess what he's looking for, is why the study of all such endomorphisms from R -> End (M) (in the modules case, let's say) should give information about R, i.e. study of these endomorphisms as a whole. Your answer seems to be focusing on each such endomorphisms, thus not quite to the point. | |
| Nov 12, 2009 at 20:21 | comment | added | Konrad Voelkel | Oh wait, maybe you're asking "how to convince somebody to use linear algebra". Then my answer would be: Don't try to. If they're happy with difficult math, let them do it. | |
| Nov 12, 2009 at 20:20 | comment | added | Konrad Voelkel | Yes, group actions are interesting in their own right. Representations are just the linear ones, thus easier to understand. The same holds for End(M) above. You could say to the unimpressed mathematician "you don't think linear algebra is useful?". | |
| Nov 12, 2009 at 20:17 | comment | added | Qiaochu Yuan | In other words, your answer does not tell me why representations of groups are more interesting than group actions. | |
| Nov 12, 2009 at 20:16 | comment | added | Qiaochu Yuan | Sure, but my point is why distinguish sources of the form End(M)? | |
| Nov 12, 2009 at 20:08 | history | answered | Konrad Voelkel | CC BY-SA 2.5 |