Timeline for Baer's criterion for projective modules
Current License: CC BY-SA 3.0
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| Mar 12, 2013 at 18:27 | comment | added | Rishi Vyas | For the restriction to finitely generated $P$, why can't we just take $Q$ to be $R$, where $R$ is our ring? The projectivity domain of a fg module is closed under arbitrary direct sums, and projectivity domains are always closed under epimorphic images, so a fg module is projective relative to $R$ iff it is projective. On the other hand, if you assume that your ring is (right, say) noetherian, it's possible to modify Torsten's initial comment to conjure up a cogenerator example that works for fg modules: choose an indecomposable injective from each isomorphism class, and take their direct sum. | |
| Mar 12, 2013 at 14:43 | history | answered | Jeremy Rickard | CC BY-SA 3.0 |