Timeline for Hom(A,C) ⊗ Hom(B,D) injects into Hom(A⊗B,C⊗D): when? why?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 5, 2011 at 9:04 | answer | added | Martin Brandenburg | timeline score: 5 | |
| Aug 5, 2011 at 8:57 | comment | added | darij grinberg | Thanks. I assume this easily follows from "finite projective modules are direct addends of finite free modules"., | |
| Aug 5, 2011 at 4:19 | comment | added | Mahdi Majidi-Zolbanin | Regarding the second part of your question, where $k$ is a commutative ring with $1$ and $A,B,C,D$ are $k$-modules, you can find a partial answer in Bourbaki's Algebra (Chapter II, No. 4, Proposition 4), where it is proved that if one of the pairs (A,B), or (A,C), or (B,D) consists of finite projective modules, then the canonical map in question is in fact bijective. | |
| Aug 3, 2011 at 18:21 | history | edited | darij grinberg | CC BY-SA 3.0 |
added reference, now that I know that the only person I am shaming is myself
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| Aug 3, 2011 at 18:18 | vote | accept | darij grinberg | ||
| Aug 3, 2011 at 18:14 | history | edited | Anton Geraschenko | CC BY-SA 3.0 |
edited title for readability
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| Aug 3, 2011 at 18:10 | answer | added | user2035 | timeline score: 28 | |
| Aug 3, 2011 at 18:07 | answer | added | Mahdi Majidi-Zolbanin | timeline score: 0 | |
| Aug 3, 2011 at 17:17 | history | asked | darij grinberg | CC BY-SA 3.0 |