Let R be a commutative ring, M an R-module of finite length and let N be an Injective R-module with zero socle. Then why $ \text{Hom}_R(M, N) $ is zero?
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$\begingroup$ How does this question arise in your research? $\endgroup$– S. Carnahan ♦Commented Apr 21, 2013 at 5:06
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$\begingroup$ In a paper of Auslander(Isolated singularities and existence of AR sequences) What can be said if M and N are in R-mod. $\endgroup$– MaxCommented Apr 21, 2013 at 5:37
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if some hom is non-zero, then the image is a module of finite length, which allows to find an irreducible submodule in $N$ giving a contradiction.
