Let R be a commutative ring, with subring S.(adsbygoogle = window.adsbygoogle || []).push({});

Let M be an R-module.

Does there exist a S-module N such that [itex]N \otimes_S R \cong M[/itex] as R-modules? Preferably with N a sub-S-module of M?

Even better, can we choose such modules N so that if we have an R-module homomorphism

f:M --> M'it yields an S-module homomorphism

g:N --> N'so that

(with the horizontal arrows the aforementioned isomorphisms)Code (Text):N (x) R ---> M

| |

g (x) R | | f

V V

N' (x) R --> M'

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# A module problem

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