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Let $F$ be a subfield of $K$, $$\Aut(K/F)=\{ \sigma:K\to K\mid \sigma(a)=a \text{ for all } a\in F \text{ and } \sigma \text{ is a ring homomorphism}\},$$ and $$K^{\Aut(K/F)} = \{ a\in K \mid \sigma(a)=a\}.$$ Then $K$ is Galois over $F$ if $K^{\Aut(K/F)} = F$.

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• Review status: reviewed
• Last edited by John Jones on 2018-07-04 23:17:50
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