# 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 be a Galois etension of fields. Then, a **Galois module** for this extension, relative to a ring , is defined as a module over the group ring , where is the Galois group of .

In the case where , a field, this is equivalent to a linear representation of over . Thus, we also use the term **Galois representation**.