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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

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Definition

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Reference

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12F05*no label found*

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## Recent Activity

Oct 21

new question: Prime numbers out of sequence by Rubens373

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new question: Lorenz system by David Bankom

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new correction: examples and OEIS sequences by fizzie

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new correction: Define Galois correspondence by porton

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new question: how to contest an entry? by zorba

new question: simple question by parag

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag