Primary extension

In field theory, a branch of algebra, a primary extension L of K is a field extension such that the algebraic closure of K in L is purely inseparable over K.

Properties

 * An extension L/K is primary if and only if it is linearly disjoint from the separable closure of K over K.
 * A subextension of a primary extension is primary.
 * A primary extension of a primary extension is primary (transitivity).
 * Any extension of a separably closed field is primary.
 * An extension is regular if and only if it is separable and primary.
 * A primary extension of a perfect field is regular.