## You are here

Homeseparably algebraically closed field

## Primary tabs

# separably algebraically closed field

*separably algebraically closed* if every separable element of the algebraic closure of $K$ belongs to $K$.

In the case when $K$ has characteristic 0, it is separably algebraically closed if and only if it is algebraically closed.

If $K$ has positive characteristic $p$, $K$ is separably algebraically closed if and only if its algebraic closure is a purely inseparable extension of $K$.

Defines:

separably algebraically closed

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

12F05*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff

## Recent Activity

Sep 17

new question: Harshad Number by pspss

Sep 14

new problem: Geometry by parag

Aug 24

new question: Scheduling Algorithm by ncovella

new question: Scheduling Algorithm by ncovella

new question: Harshad Number by pspss

Sep 14

new problem: Geometry by parag

Aug 24

new question: Scheduling Algorithm by ncovella

new question: Scheduling Algorithm by ncovella