\begin{definition}[Definition:Scalar Ring/Module]
Let $\struct {G, +_G, \circ}_R$ be a module, where:
:$\struct {R, +_R, \times_R}$ is a ring
:$\struct {G, +_G}$ is an abelian group
:$\circ: R \times G \to G$ is a binary operation.
Then the ring $\struct {R, +_R, \times_R}$ is called the scalar ring of $\struct {G, +_G, \circ}_R$.
If the scalar ring is understood, then $\struct {G, +_G, \circ}_R$ can be rendered $\struct {G, +_G, \circ}$.
\end{definition}