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.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2012-03-30 07:48:33

**Referred to by:**

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

**Differences**(show/hide)