翻訳と辞書 Words near each other ・ Regular element of a Lie algebra ・ Regular embedding ・ Regular expression ・ Regular extension ・ Regular Force ・ Regular Fries ・ Regular grammar ・ Regular Grand Lodge of Macedonia ・ Regular graph ・ Regular grid ・ Regular Guys ・ Regular Hadamard matrix ・ Regular haircut ・ Regular homotopy ・ Regular icosahedron ・ Regular ideal ・ Regular insulin ・ Regular isotopy ・ Regular Joe ・ Regular Joe (TV series) ・ Regular John ・ Regular language ・ Regular Language description for XML ・ Regular local ring ・ Regular Lovers ・ Regular map ・ Regular map (graph theory) ・ Regular Masonic jurisdictions ・ Regular matrix ・ Regular matroid Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Regular ideal ： ウィキペディア英語版 Regular ideal In mathematics, especially ring theory, a regular ideal can refer to multiple concepts. In operator theory, a right ideal $\backslash mathfrak$ in a (possibly) non-unital ring ''A'' is said to be regular (or modular) if there exists an element ''e'' in ''A'' such that $ex\; -\; x\; \backslash in\; \backslash mathfrak$ for every $x\; \backslash in\; A$. In commutative algebra a regular ideal refers to an ideal containing a non-zero divisor.〔Non-zerodivisors in commutative rings are called ''regular elements''.〕 This article will use "regular element ideal" to help distinguish this type of ideal. A two-sided ideal $\backslash mathfrak$ of a ring ''R'' can also be called a (von Neumann) regular ideal if for each element ''x'' of $\backslash mathfrak$ there exists a ''y'' in $\backslash mathfrak$ such that ''xyx''=''x''. Finally, regular ideal has been used to refer to an ideal ''J'' of a ring ''R'' such that the quotient ring ''R''/''J'' is von Neumann regular ring.〔Burton, D.M. (1970) ``A first course in rings and ideals.'' Addison-Wesley. Reading, Massachusetts .〕 This article will use "quotient von Neumann regular" to refer to this type of regular ideal. Since the adjective ''regular'' has been overloaded, this article adopts the alternative adjectives ''modular'', ''regular element'' ''von Neumann regular'', and ''quotient von Neumann regular'' to distinguish between concepts. ==Properties and examples== 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 ideal」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.