# Definition:Separable Degree

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## Definition

Let $E/F$ be a field extension.

Let $S \subseteq E$ be the separable closure of $F$ in $E$.

The **separable degree** $[E : F]_{\operatorname{sep}}$ of $E/F$ is the degree $[S : F]$.

## Also denoted as

The **separable degree** is also denoted $[E : F]_s$