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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- Review status: reviewed
- Last edited by John Cremona on 2019-10-29 15:29:05

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**History:**(expand/hide all)

- 2019-10-29 15:29:05 by John Cremona (Reviewed)
- 2019-05-22 17:16:48 by John Jones
- 2012-03-30 07:48:33 by John Jones (Reviewed)

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