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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 Connected ring ： ウィキペディア英語版 Connected ring In mathematics, especially in the field of commutative algebra, a connected ring is a commutative ring ''A'' that satisfies one of the following equivalent conditions: * ''A'' possesses no non-trivial (that is, not equal to 1 or 0) idempotent elements; * the spectrum of ''A'' with the Zariski topology is a connected space. ==Examples and non-examples== Connectedness defines a fairly general class of commutative rings. For example, all local rings and all (meet-)irreducible rings are connected. In particular, all integral domains are connected. Non-examples are given by product rings such as Z × Z; here the element (1, 0) is a non-trivial idempotent. 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「Connected ring」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.