Subring Module is Module/Special Case

Theorem
Let $S$ be a subring of the ring $\left({R, +, \circ}\right)$. Let $\circ$ be the restriction of $\circ$ to $S \times R$.

$\left({R, +, \circ}\right)_S$ is the $S$-module obtained from $\left({R, +_R, \circ}\right)_R$ by restricting scalar multiplication.

If $R$ is a ring with unity, and $1_R \in S$, then $\left({R, +, \circ}\right)_S$ is a unitary $S$-module.