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I'm trying to prove the following statement:

If $K$ is an extension of $F$ prove that the set of elements in $K$ which are separable over $F$ forms a subfield of $K$.

I have a proof for the set of algebraic elements in $K$ forming a subfield, but I'm stuck with the separable elements.

I'm assuming I should be splitting this into cases of characteristic = 0 and characteristic $\neq$ 0. Any help? I'm at a loss.

  • 1
    It's also true that [the elements which are purely inseparable over $F$ form a subfield of $K$](http://math.stackexchange.com/questions/26778/purely-inseparable-extension).2011-12-17

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