Definition:G-Module

Definition
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.