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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 Krull ring ： ウィキペディア英語版 Krull ring In commutative algebra, a Krull ring or Krull domain is a commutative ring with a well behaved theory of prime factorization. They were introduced by . They are a higher-dimensional generalization of Dedekind domains, which are exactly the Krull domains of dimension at most 1. In this article, a ring is commutative and has unity. ==Formal definition== Let $A$ be an integral domain and let $P$ be the set of all prime ideals of $A$ of height one, that is, the set of all prime ideals properly containing no nonzero prime ideal. Then $A$ is a Krull ring if # $A\_\; \backslash in\; P$, #$A$ is the intersection of these discrete valuation rings (considered as subrings of the quotient field of $A$). #Any nonzero element of $A$ is contained in only a finite number of height 1 prime ideals. 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「Krull 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.