Galois module

Definition
Let $$L/K$$ be a Galois etension 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.