\begin{definition}[Definition:Isomorphism (Abstract Algebra)/R-Algebraic Structure Isomorphism/Module Isomorphism]
Let $R$ be a ring.
Let $\struct {G, +_G, \circ}_R$ and $\struct {H, +_H, \circ}_R$ be $R$-modules.
Let $\phi: G \to H$ be a module homomorphism.
Then $\phi$ is a '''module isomorphism''' {{iff}} $\phi$ is a bijection.
\end{definition}