Regular extension

In field theory, a branch of algebra, a field extension formula_1 is said to be regular if "k" is algebraically closed in "L" (i.e., formula_2 where formula_3 is the set of elements in "L" algebraic over "k") and "L" is separable over "k", or equivalently, formula_4 is an integral domain when formula_5 is the algebraic closure of formula_6 (that is, to say, formula_7 are linearly disjoint over "k").
Self-regular extension.
There is also a similar notion: a field extension formula_8 is said to be self-regular if formula_9 is an integral domain. A self-regular extension is relatively algebraically closed in "k". However, a self-regular extension is not necessarily regular.