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R-modules

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Suppose R is a ring, G, M are R-modules and Hom(G,M) is the set of R-module homomorphisms from G to M.
Identify Hom(Z/nZ,Z), Hom(Z,Z/nZ), Hom(Z/3Z,Z/6Z), Hom(Z/10Z,Z/6Z) as abelian groups, where n belongs to Z and Z is the set of integers.

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Solution Summary

This solution demonstrates how to prove that a set of R-module homomorphisms are abelian groups.

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