\begin{definition}[Definition:G-Module]
Let $\struct{ V, +, \cdot }$ be a vector space over a field $\struct{ k, \oplus, \circ }$.
Let $G$ be a group.
Let $\phi : G \times V \to V$ be a linear group action of $G$ on $V$.
Then $\struct{ V,\phi }$ is called a '''$G$-module'''.
Category:Definitions/Group Actions
Category:Definitions/Representation Theory
\end{definition}