Category:Galois Extensions
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This category contains results about Galois Extensions.
Definitions specific to this category can be found in Definitions/Galois Extensions.
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.