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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'').〔Fried & Jarden (2008) p.38〕〔Cohn (2003) p.425〕 ==Properties== * Regularity is transitive: if ''F''/''E'' and ''E''/''K'' are regular then so is ''F''/''K''.〔Fried & Jarden (2008) p.39〕 * If ''F''/''K'' is regular then so is ''E''/''K'' for any ''E'' between ''F'' and ''K''.〔 * The extension ''L''/''k'' is regular if and only if every subfield of ''L'' finitely generated over ''k'' is regular over ''k''.〔 * Any extension of an algebraically closed field is regular.〔〔Cohn (2003) p.426〕 * An extension is regular if and only if it is separable and primary.〔Fried & Jarden (2008) p.44〕 * A purely transcendental extension of a field is regular. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「regular extension」の詳細全文を読む スポンサード リンク
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