Timeline for the relation between projective and quasi-projective modules
Current License: CC BY-SA 3.0
3 events
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| Jun 27, 2016 at 3:37 | comment | added | Jeremy Rickard | @abx If $M$ is a non-semisimple right $R$-module, pick $m\in M$ not in the socle, and let $I<R$ be a maximal right ideal containing the annihilator of $m$. Then $R\to R/I$ is a non-split epimorphism to a simple module, and so $R/I$ is a non-projective simple module. | |
| Jun 26, 2016 at 13:26 | comment | added | abx | @Jeremy Rickard : Do you have a reference (or a proof) for the fact that projectivity of simple modules implies semi-simplicity? | |
| Jun 26, 2016 at 10:22 | history | answered | Jeremy Rickard | CC BY-SA 3.0 |