\begin{definition}[Definition:Scalar Ring/Vector Space over Division Ring]
Let $\struct {G, +_G, \circ}_K$ be a vector space over a division ring, where:
:$\struct {K, +_K, \times_K}$ is a division ring
:$\struct {G, +_G}$ is an abelian group $\struct {G, +_G}$
:$\circ: K \times G \to G$ is a binary operation.
Then the division ring $\struct {K, +_K, \times_K}$ is called the '''scalar division ring''' of $\struct {G, +_G, \circ}_K$, or just '''scalar ring'''.
If the '''scalar division ring''' is understood, then $\struct {G, +_G, \circ}_K$ can be rendered $\struct {G, +_G, \circ}$.
Category:Definitions/Vector Algebra
\end{definition}