Timeline for How to introduce notions of flat, projective and free modules?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Nov 19, 2010 at 3:41 | comment | added | Charles Rezk | (every homomorphism from a finitely presented module to $M$, of course) | |
| Nov 19, 2010 at 3:39 | comment | added | Charles Rezk | The equational criterion more or less amounts to the statement: "$M$ is flat IFF every homomorphism from a finitely presented module factors through a free module". (With the instant consequence that flat & finitely presented imply projective.) | |
| Nov 19, 2010 at 3:19 | comment | added | Pete L. Clark | @Andreas: right, this is the "equational criterion of flatness" that Manny Reyes referred to above. I do plan on covering it (it's in my private copy of my notes, although not yet the one posted on my webpage) because it's used to prove that a finitely generated flat module over a local ring is projective. I admit though that I don't have a lot of intuition for what this criterion "really means". Any further hints would be appreciated. | |
| Nov 18, 2010 at 22:59 | history | answered | Andreas Blass | CC BY-SA 2.5 |