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).

单词	Regular extension
释义	Regular extension 英语百科 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).
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