Definition:Reducible G-Module

This article needs to be linked to other articles. In particular: In particular, the proper definition of G-module to be found (the existing links are to $R$-module, which is a module over the ring, not the group). Links to linear representations do not obviously link to the definitions in this particular context. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding these links. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{MissingLinks}} from the code.

Definition

Let $M$ be a $G$-module.

Then $M$ is reducible if and only if the corresponding linear representation is reducible.

Also see

In Correspondence between Linear Group Actions and Linear Representations, it is shown that linear representations and $G$-modules are bijective.