环的广义Noether性(英)

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．     

特征模对环的刻划

设Ｒ是一个环，Ｍ是一个左Ｒ摸，Ｍ＊＝ＨｏｍＺ（Ｍ，Ｑ／Ｚ）为Ｍ的特征模．Ｒ．Ｒ．Ｃｏｌｂｙ和Ｔ．Ｊ．Ｃｈｏａｔｈａｎ等人利用特征模对ＩＦ环、凝聚环、Ｎｏｅｔｈｅｒ环、Ａｒｔｉｎ环作出了一些非常好的刻划．本文利用特征模对更为广泛的一些环作出了较有意义的刻划．     

局部几乎完全整环的几点注记

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.     

关于自内射环的一个注记

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     

关于SF—环的几点注记

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。     

IF环和拟ZIF环

本文定义了拟ＺＩＦ环．研究了ＩＦ环与拟ＺＩＦ环的结构．进一步地，讨论了ＩＦ环与拟ＺＩＦ环的关系，并用拟ＺＩＦ环刻划了ＩＦ环．     

关于拟平坦模的几个注记

本文所有的环均指有单位元的环,模均指酉模。左R-模M称为拟内射的,如果对任意N相似文献   

关于AP-内射环的一个注记

本文的主要目的是讨论AP-内射环中的两个问题:(1)环R是正则的当且仅当R是左AP-内射的左PP-环;(2)如果R是左AP-内射环,那么R是内射环当且仅当R是弱内射环.因此我们推广了内射环的一些结果,与此同时我们还取得了一些新的结果.     

广义FP—内射模、广义平坦模与某些环

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。     

一类广义遗传环

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。     

FI性质的传递

一个环R称为左(右)FI环，如果它的每一个平坦左(右)R模是内射的，R称为FI环是指它既是左且右的FI环．本讨论了当R是FI环时，其多项式环R[t]，矩阵环MN(R)以及分式不S^-1R也是FI环的充分与必要条件．     

Gorenstein同调维数和环变换

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.     

On Serial Noetherian Rings

It is well known that every serial Noetherian ring satisfies the restricted minimum condition. In particular, following Warfield (1975 Warfield , R. B. ( 1975 ). Serial rings and finitely presented modules . J. Algebra 37 : 187 – 222 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]), 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.     

On Flatness and Completion for Infinitely Generated Modules over Noetherian Rings

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.     

Localization of Injective Modules Over Arithmetical Rings

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.     

Noetherian Skew Group Rings of F.C Groups

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.     

Gorenstein Injective and Gorenstein Flat Resolution of Modules Over Gorenstein Rings

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.     

n- Gorenstein环上的 Gorenstein内射模(英文)

用 Gorenstein内射模刻画了 n-Gorenstein环 .