# Definition:Separable Closure

## Definition

Let $K$ be a field.

A **separable closure** of $K$ is a separably closed algebraic field extension of $F$.

It may be defined as the relative separable closure of $F$ in its algebraic closure.

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Let $K$ be a field.

A **separable closure** of $K$ is a separably closed algebraic field extension of $F$.

It may be defined as the relative separable closure of $F$ in its algebraic closure.

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