Definition:Restriction of Scalars of Module

Definition
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 $\rho \circ f$.

Also see

 * Definition:Extension of Scalars of Module