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is every finitely n-presented (S^{-1})R-module a localization of a finitely n-presented R-module?
Let S be a multiplicative set in a ring R. We can see that every finitely generated $(S^{-1})R$-module is a localization of a finitely generated R-module.
Then, more generally, is every finitely n-...
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modules whose every submodule is a homomorphic image
Let $R$ be a commutative ring with unity. Let us say that an $R$-module $M$ satisfies property $\mathcal P$ if every submodule of $M$ is a homomorphic image of $M$.
Can we characterize all ...