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 SeparablyAlgebraicallyClosedField 2013-03-22 15:58:30 2013-03-22 15:58:30 polarbear (3475) polarbear (3475) 6 polarbear (3475) Definition msc 12F05 separably algebraically closed