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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 Goldman domain ： ウィキペディア英語版 Goldman domain In mathematics, a Goldman domain is an integral domain ''A'' whose field of fractions is a finitely generated algebra over ''A''.〔Goldman domains/ideals are called G-domains/ideals in (Kaplansky 1974).〕 They are named after Oscar Goldman. An overring (i.e., an intermediate ring lying between the ring and its field of fractions) of a Goldman domain is again a Goldman domain. There exists a Goldman domain where all nonzero prime ideals are maximal although there are infinitely many prime ideals.〔Kaplansky, pp. 13〕 An ideal ''I'' in a commutative ring ''A'' is called a Goldman ideal if the quotient ''A''/''I'' is a Goldman domain. A Goldman ideal is thus prime, but not necessarily maximal. In fact, a commutative ring is a Jacobson ring if and only if every Goldman ideal in it is maximal. The notion of a Goldman ideal can be used to give a slightly sharpened characterization of a radical of an ideal: the radical of an ideal ''I'' is the intersection of all Goldman ideals containing ''I''. == Notes == 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「Goldman domain」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.