Definition:Vector Space over Division Subring/Special Case

Theorem
Let $S$ be a division subring of the ring with unity $\left({R, +, \circ}\right)$ whose unity is $1_R$ such that $1_R \in S$.

Then $\left({R, +, \circ}\right)_S$ is an $S$-vector space, where $\circ$ is the restriction of $\circ$ to $S \times R$.