Lesson plan
Regular extension
In field theory, a branch of algebra, a field extension L/k is said to be regular if k is algebraically closed in L (i.e., k = \hat k where \hat k is the set of elements in L algebraic over k) and L is separable over k, or equivalently, L \otimes_k \overline{k} is an integral domain when \overline{k} is the algebraic closure of k (that is, to say, L, \overline{k} are linearly disjoint over k).
Article summary
In field theory, a branch of algebra, a field extension L/k is said to be regular if k is algebraically closed in L (i.e., k = \hat k where \hat k is the set of elements in L algebraic over k) and L is separable over k, or equivalently, L \otimes_k \overline{k} is an integral domain when \overline{k} is the algebraic closure of k (that is, to say, L, \overline{k} are linearly disjoint over k).
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Discussion questions
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