翻訳と辞書 Words near each other ・ Idelson ・ Ideluy ・ Ideluy-e Olya ・ Ideluy-e Sofla ・ Idem ・ Idem Paris ・ Idem sonans ・ Idemili North ・ Idemili South ・ Idemitsu (disambiguation) ・ Idemitsu Kosan ・ Idemitsu Museum of Arts ・ IDempiere ・ Idempotence ・ Idempotency of entailment ・ Idempotent element ・ Idempotent matrix ・ Idempotent measure ・ Idempotent relation ・ IDEmøbler ・ IDEN ・ Iden ・ Iden (disambiguation) ・ Iden Green ・ Iden, East Sussex ・ Iden, Saxony-Anhalt ・ Idenau ・ Idenheim ・ Ident ・ Ident protocol 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 Idempotent element ： ウィキペディア英語版 Idempotent element In abstract algebra, an element ''x'' of a set with a binary operation ∗ is called an idempotent element (or just an idempotent) if . This reflects the idempotence of the binary operation on that particular element. Idempotents are especially prominent in ring theory. For general rings, elements idempotent under multiplication are tied with decompositions of modules, as well as to homological properties of the ring. In Boolean algebra, the main objects of study are rings in which all elements are idempotent under both addition and multiplication. ==Definitions== An idempotent element of a ring is an element ''a'' such that .〔See Hazewinkel et al. (2004), p. 2.〕 That is, the element is idempotent under the ring's multiplication. Inductively then, one can also conclude that for any positive integer ''n''. There are many special types of idempotents defined after the following examples section. 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「Idempotent element」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.