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 local and global number fields are separable.

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**Knowl status:**

- Review status: beta
- Last edited by John Jones on 2012-03-30 07:48:33.052000