Definition:Galois Extension

Definition

Let $L / K$ be a finite field extension.

Finite Galois Extension

$L / K$ is a (finite) Galois extension if and only if the fixed field of its automorphism group is $K$:

$\map {\operatorname{Fix}_L} {\Gal {L / K} } = K$

Arbitrary Galois Extension

$L / K$ is a Galois extension if and only if it is normal and separable.

Also see

• Fundamental Theorem of Galois Theory
• Definition:Galois Closure

• Results about Galois extensions can be found here.

Source of Name

This entry was named for Évariste Galois.

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