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Homeseparably algebraically closed field

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# separably algebraically closed field

*separably algebraically closed* if every separable element of the algebraic closure of $K$ belongs to $K$.

In the case when $K$ has characteristic 0, it is separably algebraically closed if and only if it is algebraically closed.

If $K$ has positive characteristic $p$, $K$ is separably algebraically closed if and only if its algebraic closure is a purely inseparable extension of $K$.

Defines:

separably algebraically closed

Type of Math Object:

Definition

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Reference

## Mathematics Subject Classification

12F05*no label found*

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