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.