\begin{definition}[Definition:Scalar Multiplication/R-Algebraic Structure]
Let $\struct {S, *_1, *_2, \ldots, *_n, \circ}_R$ be an $R$-algebraic structure with $n$ operations, where:
:$\struct {R, +_R, \times_R}$ is a ring
:$\struct {S, *_1, *_2, \ldots, *_n}$ is an algebraic structure with $n$ operations
The operation $\circ: R \times S \to S$ is called '''scalar multiplication'''.
\end{definition}