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Let R be a commutative ring, with subring S.
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
(with the horizontal arrows the aforementioned isomorphisms)
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 homomorphismg:N --> N'
so that
Code:
N (x) R ---> M
| |
g (x) R | | f
V V
N' (x) R --> M'
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