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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 Tertiary ideal ： ウィキペディア英語版 Tertiary ideal In mathematics, a tertiary ideal is an (two-sided) ideal in a (perhaps noncommutative) ring that cannot be expressed as a nontrivial intersection of a right fractional ideal with another ideal. Tertiary ideals generalize primary ideals to the case of noncommutative rings. Although primary decompositions do not exist in general for ideals in noncommutative rings, tertiary decompositions do, at least if the ring is Noetherian. Every primary ideal is tertiary. Tertiary ideals and primary ideals coincide for commutative rings. To any (two-sided) ideal, a tertiary ideal can be associated called the tertiary radical, defined as :$t(I)\; =\; \backslash \; \backslash forall\; s\; \backslash notin\; I,\; \backslash mbox\backslash exists\; x\; \backslash in\; (s)\backslash mbox\; x\; \backslash notin\; I\; \backslash text\; (x)(r)\; \backslash subset\; I\; \backslash \}.\; \backslash ,$ Then ''t''(''I'') always contains ''I''. If ''R'' is a (not necessarily commutative) Noetherian ring and ''I'' a right ideal in ''R'', then ''I'' has a unique irredundant decomposition into tertiary ideals :$I\; =\; T\_1\; \backslash cap\; \backslash dots\; \backslash cap\; T\_n$. == See also == * Primary ideal * Lasker - Noether theorem 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「Tertiary 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.