共查询到18条相似文献,搜索用时 46 毫秒
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众所周知,环R是右Noether的当且仅当任意内射右R-模的直和是内射的.本文我们将用Ne-内射模和U-内射模来刻画Ne-Noether环和U-Noether环. 相似文献
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整环$R$被称为局部几乎完全整环, 指的是对任意极大理想${\frak m}$都有$R_{{\frak m}}$是几乎完全整环. 本文利用局部完全环, 几乎投射模, 弱内射模, 几乎强平坦模和强Matlis余挠模给出了局部几乎完全整环的若干等价刻画. 相似文献
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黄平安 《数学的实践与认识》2003,33(4):107-109
设 R是含幺环 ,本文证明了在一定条件下 ,R与其一种有限单扩张同时具有自内射性 ,从而将欧海文等的主要结果定理 1推广到更大一类环上 相似文献
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关于SF—环的几点注记 总被引:1,自引:0,他引:1
文中,我们证明了如下主要结果:Ⅰ对于环R,下面条件是等价的:(1)R是Artin半单环;(2)R是左SF-环,且R满足特殊右零化子降链条件;(3)R是左SF-环和Ⅰ-环,且R^R具有有限Goldie维数。Ⅱ对于环R,下面条件是等价:(1)R是Von Neumann正则环;(2)R是左SF-环,且每个奇异循环左R-模的极大子模是平坦的。 相似文献
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广义FP—内射模、广义平坦模与某些环 总被引:2,自引:0,他引:2
左(右)R-模A称为GFP-内射模,如果ExtR(M,A)=0对任-2-表现R-模M成立;左(右)R-模称为G-平坦的,如果Tor1^R(M,A)=0(Tor1^R(AM)=0)对于任一2-表现右(左)R-模M成立;环R称左(右)R-半遗传环,如果投射左(右)R-模的有限表现子模是投射的,环R称为左(右)G-正而环,如果自由左(右)R-模的有限表现子模为其直和项,研究了GFP-内射模和G-平坦模的一些性质,给出了它们的一些等价刻划,并利用它们刻划了凝聚环,G-半遗传环和G-正则环。 相似文献
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一类广义遗传环 总被引:2,自引:0,他引:2
朱占敏 《纯粹数学与应用数学》2003,19(1):68-71
称环R为左亚遗传环,如果内射左R-模的商模是FG-内射的,给出了左亚遗传环的一些刻划,给出了左亚遗传环的半单环的条件,并研究了左亚遗传环的一些性质。 相似文献
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In this paper,we shall be concerned with what happens of Gorenstein homological dimensions when certain modifications are made to a ring.The five structural operations addressed later are the formation of excellent extensions,localizations,Morita equivalences,polynomial extensions and power series extensions. 相似文献
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It is well known that every serial Noetherian ring satisfies the restricted minimum condition. In particular, following Warfield (1975), such a ring is a direct sum of an Artinian ring and hereditary prime rings. The aim of this note is to show that every serial ring having the restricted minimum condition is Noetherian. 相似文献
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Amnon Yekutieli 《代数通讯》2013,41(11):4221-4245
Let A be a noetherian commutative ring, and let 𝔞 be an ideal in A. We study questions of flatness and 𝔞-adic completeness for infinitely generated A-modules. This is done using the notions of decaying function and 𝔞-adically free A-module. 相似文献
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François Couchot 《代数通讯》2013,41(10):3418-3423
It is proved that localizations of injective R-modules of finite Goldie dimension are injective if R is an arithmetical ring satisfying the following condition: for every maximal ideal P, R P is either coherent or not semicoherent. If, in addition, each finitely generated R-module has finite Goldie dimension, then localizations of finitely injective R-modules are finitely injective too. Moreover, if R is a Prüfer domain of finite character, localizations of injective R-modules are injective. 相似文献
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Let R *θG be the skew group ring with a F.C group G and the group homom-rphismθfrom G to Aut(R), the group of automorphisms of the ring R. In this paper,the necessary and sufficient condition such that R*θG will be Noetherian is given, which generalizes the results of I.G. connel. 相似文献
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《代数通讯》2013,41(11):4415-4432
Abstract Let R be a commutative Noetherian ring. There are several characterizations of Gorenstein rings in terms of classical homological dimensions of their modules. In this paper, we use Gorenstein dimensions (Gorenstein injective and Gorenstein flat dimension) to describe Gorenstein rings. Moreover a characterization of Gorenstein injective (resp. Gorenstein flat) modules over Gorenstein rings is given in terms of their Gorenstein flat (resp. Gorenstein injective) resolutions. 相似文献
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用 Gorenstein内射模刻画了 n-Gorenstein环 . 相似文献