separably algebraically closed field


A field K is called separably algebraically closed if every separable element of the algebraic closureMathworldPlanetmath of K belongs to K.
In the case when K has characteristicPlanetmathPlanetmath 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