Regular extension

In field theory, a branch of algebra, a field extension is said to be regular if k is algebraically closed in L (i.e., where is the set of elements in L algebraic over k) and L is separable over k, or equivalently, is an integral domain when is the algebraic closure of (that is, to say, are linearly disjoint over k).[1][2]


Self-regular extension

There is also a similar notion: a field extension is said to be self-regular if is an integral domain. A self-regular extension is relatively algebraically closed in k.[6] However, a self-regular extension is not necessarily regular.


  1. Fried & Jarden (2008) p.38
  2. 1 2 Cohn (2003) p.425
  3. 1 2 3 Fried & Jarden (2008) p.39
  4. Cohn (2003) p.426
  5. Fried & Jarden (2008) p.44
  6. Cohn (2003) p.427

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