Category:Definitions/Finite Galois Extensions
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This category contains definitions related to Finite Galois Extensions.
Related results can be found in Category:Finite Galois Extensions.
Let $L / K$ be a finite field extension.
Definition 1
$L / K$ is a (finite) Galois extension if and only if the fixed field of its automorphism group is $K$:
- $\map {\operatorname{Fix}_L} {\Gal {L / K} } = K$
Definition 2
$L / K$ is a (finite) Galois extension if and only if it is normal and separable.
Definition 3
$L / K$ is a (finite) Galois extension if and only if the order of the automorphism group $\Aut {L / K}$ equals the degree $\index L K$:
- $\order {\Aut {L / K} } = \index L K$
Pages in category "Definitions/Finite Galois Extensions"
The following 5 pages are in this category, out of 5 total.