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If $K/F$ is a finite degree field extension, $\alpha\in K$ is separable over $F$ if its monic irreducible polynomial has distinct roots in the algebraic closure $\overline{F}$.

The extension $K/F$ is separable if every $\alpha\in K$ is separable over $F$.

All algebraic extensions of local and global number fields are separable.

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• Last edited by John Cremona on 2019-10-29 15:29:05
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