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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 Jaffard ring ： ウィキペディア英語版 Jaffard ring In mathematics, a Jaffard ring is a type of ring, more general than a Noetherian ring, for which Krull dimension behaves as expected in polynomial extensions. They are named for Paul Jaffard who first studied them in 1960. Formally, a Jaffard ring is a ring ''R'' such that the polynomial ring :$\backslash dim\; R()\; =\; n\; +\; \backslash dim\; R,\; \backslash ,$ where "dim" denotes Krull dimension. A Jaffard ring that is also an integral domain is called a Jaffard domain. The Jaffard property is satisfied by any Noetherian ring ''R'', so examples of non-Jaffardian rings are quite difficult to find. Nonetheless, an example was given in 1953 by Abraham Seidenberg: the subring of :$\backslash overline\{\backslash mathbf\{Q\}\}T$ consisting of those formal power series whose constant term is rational. ==References== * * * 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「Jaffard 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.