Timeline for $P$ is projective if and only if $P\otimes N\cong Hom(Hom(P,R),N)$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2019 at 5:25 | vote | accept | tessellation | ||
| S Feb 2, 2019 at 21:50 | history | suggested | ssx |
Inappropriate tags removed
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| Feb 2, 2019 at 15:05 | review | Close votes | |||
| Feb 8, 2019 at 3:05 | |||||
| Feb 2, 2019 at 14:35 | answer | added | abx | timeline score: 6 | |
| Feb 2, 2019 at 14:28 | review | Suggested edits | |||
| S Feb 2, 2019 at 21:50 | |||||
| Feb 2, 2019 at 10:12 | comment | added | Praphulla Koushik | which way are you comfortable with? | |
| Feb 2, 2019 at 8:51 | history | edited | tessellation | CC BY-SA 4.0 |
added 39 characters in body
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| Feb 2, 2019 at 8:42 | comment | added | Sasha | You should construct a natural transformation (in $N$) in one direction. Then consider the subclass of all objects on which the natural transformation is an isomorphism. Then check whether $R$ is in this subclass, and other things (if two objects from a short exact sequence are in the subclass, is the third as well?). Also, is the subclass closed under infinite direct sums? This will give you a feeling for the question, for which $N$ to expect an isomorphism (a finitely generated $N$ is the cokernel of a morphism between finite direct sums of $R$'s, etc.). | |
| Feb 2, 2019 at 8:00 | comment | added | abx | Do you mean for all finitely generated modules $N$? Otherwise this is clearly false. | |
| Feb 2, 2019 at 7:50 | history | asked | tessellation | CC BY-SA 4.0 |