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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Regular extension ： ウィキペディア英語版 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., $k\; =\; \backslash hat\; k$ where $\backslash hat\; k$ is the set of elements in ''L'' algebraic over ''k'') and ''L'' is separable over ''k'', or equivalently, $L\; \backslash otimes\_k\; \backslash overline$ is an integral domain when $\backslash overline$ is the algebraic closure of $k$ (that is, to say, $L,\; \backslash overline$ 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 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.