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. References

 

Field (mathematics)