\begin{definition}[Definition:Restriction of Scalars of Module]
Let $R$ and $S$ be commutative rings with unity.
Let $f : R \to S$ be a ring homomorphism.
Let $M$ be an $S$-module with ring representation $\rho$.
The '''restriction of scalars''' of $M$ to $R$ via $f$ is the $R$-module with ring representation $\rho \circ f$.
\end{definition}