Galois module

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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 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.