show · nf.separable all knowls · up · search:

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.

Knowl status:
  • Review status: reviewed
  • Last edited by John Cremona on 2019-10-29 15:29:05
Referred to by:
History: (expand/hide all) Differences (show/hide)