I came across the following theorem in homomorphisms of modules, which I couldn't understand beyond symbolic and set theoretic verifications.
Let $M$ be a left $R$-module and $G$ an abelian group. Then $\rm{Hom}_{\mathbb{Z}}(R,G)$ is a left $R$-module via the right $R$-module structure of $R$. Then there is an isomorphism of abelian groups $$\rm{Hom}_R(M,\rm{Hom}_{\mathbb{Z}}(R,G))\rightarrow \rm{Hom}_{\mathbb{Z}}(M,G).$$
My obvious question is what should we understand from this isomorphism? Another question is, at what places such situations occurs? I mean, can one illustrate this theorem with some special case or example?