Timeline for Modules "projective in a subcategory"
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| May 29, 2014 at 17:40 | comment | added | Jeremy Rickard | By the way, for finite dimensional local algebras $A$ over a field, the fact that projective modules are free is much more elementary than Kaplansky's theorem. For any module $M$, the obvious map $F=A\otimes_k\operatorname{head}(M)\to\operatorname{head}(M)$ lifts to a surjection $F\to M$, which splits if $M$ is projective, in which case the kernel is zero since its head is zero. | |
| May 28, 2014 at 13:23 | comment | added | Tom Bachmann | I'll think about your proof after i had breakfast. This is the best possible answer I could hope for! (I know "thank you" comments are frowned upon, but I just love mathoverflow right now.) | |
| May 28, 2014 at 13:21 | history | edited | Jeremy Rickard | CC BY-SA 3.0 |
corrected "not equals" to "equals"
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| May 28, 2014 at 13:20 | vote | accept | Tom Bachmann | ||
| May 28, 2014 at 12:51 | history | answered | Jeremy Rickard | CC BY-SA 3.0 |