Galois module

This term is related to: Galois theory
View other terms related to Galois theory | View facts related to Galois theory

This term is related to: linear representation theory
View other terms related to linear representation theory | View facts related to linear representation theory

Definition

Let $L/K$ be a Galois extension of fields. Then, a Galois module for this extension, relative to a ring $R$, is defined as a module over the group ring $R[G]$, where $G$ is the Galois group of $L/K$.

In the case where $R=k$, a field, this is equivalent to a linear representation of $G$ over $k$. Thus, we also use the term Galois representation.