\begin{definition}[Definition:Scalar Addition/Vector Space]
Let $\struct {K, +_K, \times_K}$ be a field.
Let $\struct {G, +_G}$ be an abelian group.
Let $V := \struct {G, +_G, \circ}_K$ be the corresponding '''vector space over $K$'''.
The field addition operation $+_K$ on $V$ is known as '''scalar addition''' on $V$.
Category:Definitions/Vector Spaces
Category:Definitions/Scalar Addition
\end{definition}