Definition:Galois Extension

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Definition

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


Finite Galois Extension

$L/K$ is a 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


Source of Name

This entry was named for √Čvariste Galois.


Sources