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Results tagged with projective-modules
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user 35416
For questions about projective modules over a ring and projective objects in related categories.
4
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injective hull and projective cover of simple modules are indecomposable
One definition of "projective cover" of $S$ is that it is a projective module $P$, together with an epimorphism $\phi\colon P\to S$ such that the kernel $K$ is a superfluous submodule of $P$, meaning …
- 13k
7
votes
Must a finitely generated projective module over a group ring with vanishing coinvariants be...
This is true when $G$ is finite. This follows from a theorem of Swan [1], which asserts that all projective $\mathbb{Z}[G]$-modules are locally free, i.e isomorphic to a free module over $\mathbb{Z}_p …
- 13k