separably algebraically closed field

A field $K$ is called 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 $K$.

Title	separably algebraically closed field
Canonical name	SeparablyAlgebraicallyClosedField
Date of creation	2013-03-22 15:58:30
Last modified on	2013-03-22 15:58:30
Owner	polarbear (3475)
Last modified by	polarbear (3475)
Numerical id	6
Author	polarbear (3475)
Entry type	Definition
Classification	msc 12F05
Defines	separably algebraically closed