 Galois closure of a field extension (source code)

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= Galois closure of a field extension
{c}
{title2=$M/K$}

= Galois closure
{c}
{synonym}

The Galois closure of a finite separable extension $L/K$ is the smallest <Galois extension> in a fixed separable closure containing $L$. It is generated by all the conjugates of $L$. If $G=\operatorname{Gal}(M/K)$ and $H=\operatorname{Gal}(M/L)$, their <subgroup core> is trivial. This is distinct from the existing group-theoretic <normal closure>.

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