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.Fried & Jarden (2008) p.44
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.
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