翻訳と辞書 Words near each other ・ Zarina Zabrisky ・ Zarinaea ・ Zarindasht ・ Zarine Khan ・ Zarine Kharas ・ Zarinja ・ Zarinsk ・ Zarinsky ・ Zarinsky District ・ Zariphios School ・ Zariquieya ・ Zariqum ・ Zarir ・ Zarishat ・ Zariski geometry ・ Zariski ring ・ Zariski space ・ Zariski surface ・ Zariski tangent space ・ Zariski topology ・ Zariski's connectedness theorem ・ Zariski's lemma ・ Zariski's main theorem ・ Zariski–Riemann space ・ Zaritap ・ Zaritsky ・ Zariun ・ Zarivar Rural District ・ Zarivaran ・ Zariver Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Zariski ring ： ウィキペディア英語版 Zariski ring In commutative algebra, a Zariski ring is a commutative Noetherian topological ring ''A'' whose topology is defined by an ideal ''m'' contained in the Jacobson radical, the intersection of all maximal ideals. They were introduced by under the name "semi-local ring" which now means something different, and named "Zariski rings" by . Examples of Zariski rings are noetherian local rings and $\backslash mathfrak\; a$-adic completions of noetherian rings. Let ''A'' be a noetherian ring and $\backslash widehat$ its $\backslash mathfrak\; a$-adic completion. Then the following are equivalent. * $\backslash widehat$ is faithfully flat over ''A'' (in general, only flat over it). * Every maximal ideal is closed for the $\backslash mathfrak\; a$-adic topology. * ''A'' is a Zariski ring. ==References== * M. Atiyah, I. Macdonald ''Introduction to commutative algebra'' Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969 * * * 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「Zariski 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.