\begin{definition}[Definition:R-Algebraic Structure]
Let $\struct {R, +_R, \times_R}$ be a ring.
Let $\struct {S, \ast_1, \ast_2, \ldots, \ast_n}$ be an algebraic structure with $n$ operations.
Let $\circ: R \times S \to S$ be a binary operation.
Then $\struct {S, \ast_1, \ast_2, \ldots, \ast_n, \circ}_R$ is an '''$R$-algebraic structure with $n$ operations'''.
If the number of operations in $S$ is either understood or general, it is just called an '''$R$-algebraic structure''', and the structure can be denoted $\struct {S, \circ}_R$.
\end{definition}