The connes spectrums of certain finite non-abelian groups

In this article, we investigate when every simple module has a projective (pre)envelope. It is proven that (1) every simple right R-module has a projective preenvelope if and only if the left annihilator of every maximal right ideal of R is finitely generated; (2) every simple right R-module has an epic projective envelope if and only if R is a right PS ring; (3) Every simple right R-module has a monic projective preenvelope if and only if R is a right Kasch ring and the left annihilator of every maximal right ideal of R is finitely generated.     

FGF group rings

Periodica Mathematica Hungarica - A ring R is called a left FGF ring if every finitely generated left R-module can be embedded in a free left R-module. It is proved that a group ring RG is left FGF...     

关于E_ω-投射模和E_ω-内射模(英文)

左R-模M称为Eω-内射模,如果对环R中任意的ω阶Euclid理想I来说,任何R-模同态能够拓展为R-模同态。左R-模M称为Eω-投射模,若对环R中任意的ω阶Euclid理想I和任何R-模同态f∈HomR(M,R/I),存在R-模同态g∈HomR(M,R)使得f=πg,其中π是自然同态。本文证明P和Q均是Eω-投射模当且仅当PQ是Eω-投射模。进而,又证明了每一个左R-模是Eω-投射的当且仅当每一个左R-模是Eω-内射。     

Characterizations of F-V-rings by Quasi-continuous Modules

ＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｓｏｆＦ－Ｖ－ｒｉｎｇｓｂｙＱｕａｓｉ－ｃｏｎｔｉｎｕｏｕｓＭｏｄｕｌｅｓＬｉｕＺｈｏｎｇｋｕｉ（刘仲奎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｕｅｓｔＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｃｈ...     

内射模的t－平坦性

设Ｒ为环，ｔ是左Ｒ－模范畴的一个遗传挠理论．文中证明了下述各点等价：（１）每个内射左Ｒ－模是ｔ－平坦的；（２）每个ｔ－有限表现左Ｒ－模的内射包络是ｔ－平坦的；（３）每个ｔ－有限表现左Ｒ－模是自由Ｒ－模的子模；（４）每个ｔ－有限表现左Ｒ－模是自反的且其对偶模是Ｈ－有限生成的．     

关于所有子模是纯子模的平坦模

引进了一新模类-完全平坦模(每一个商模平坦).并得到了:令M是平坦左R-模,RM是完全平坦模当且仅当RM的所有子模是纯的当且仅当每一个右R-模A是M-平坦的.同时本文用完全平坦模刻画了V.N.正则环.     

投射可迁环上矩阵环的若当同态

设R′是一个环,Mn′（R′）是R′上的n′×n′矩阵环.如果环R有不变基数性质并且每个有限生成的投射左R-模是自由模,则R是一个投射自由环.如果环R≌Mr（S）,其中S是一个投射自由环,则R是一个投射可迁环.当R是一个投射可迁环时,给出了从Mn′（R′）到Mn（R）（n′≥n≥2）的若当同态的代数公式.     

Artin半单环的特征

本文证明了如下结果：环Ｒ是Ａｒｔｉｎ半单的当且仅当存在一个基数ｃ，使得任意左Ｒ－模是一个连续模和一个ｃ－限制的ＥＳ－模的直和，也当且仅当存在一个基数ｃ，使得任意左界Ｒ－模是一个拟投射模和一个ｃ－限制的ＥＳ－模的直和。     

ON ORDER RINGS OF SEMI-PRIMARY RINGS

The main results of this paper are stated as follows.Let R be an orderring in thesemi-primary ring Q.Suppose that R satisfies the maximal condition for nil right ideals ofR,Then we have(i)if an ideal I of R has a finite length as right R-module,then I alsohas a finite length as left R-module;(ii)denote by A(R)the Artinian radical of R,andN the nil radical of R,then A(R)+N/N=A(R/N),if R satisfies the commutative condi-tion on the zero product of prime ideals of B.     

FP-内射环的一个特征

本文首次利用投射模给出了右ＦＰ-内射环的一个外部特征，即Ｒ为右ＦＰ-内射环当且仅当投射左Ｒ-模的有限生成子模为闭子模。     

Gorenstein dimensions of unbounded complexes and change of base (with an appendix by Driss Bennis)

For a commutative ring R and a faithfully flat R-algebra S we prove,under mild extra assumptions,that an R-module M is Gorenstein flat if and only if the left S-module S?_R M is Gorenstein flat,and that an R-module N is Gorenstein injective if and only if it is cotorsion and the left S-module Hom R(S,N)is Gorenstein injective.We apply these results to the study of Gorenstein homological dimensions of unbounded complexes.In particular,we prove two theorems on stability of these dimensions under faithfully flat (co-)base change.     

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。     

关于拟P-内射模的一些注记(英文)

设 R是一个环 .一个右 R-模 M叫做拟 P-内射的 ,如果 M的每个 M-循环子模到 M的任一个 R-同态都能扩展到 M.假设 M是一个自生成子的拟 P-内射模 .在这篇文章中 ,我们表明如果这样一个模是一个 CF-模 (特别地 ,CS-模 ) ,那么 S/J(S)是正则的 ,其中 S=End(MR) .进一步 ,如果 S是半素环 ,那么 M的每个极大核是 M的一个直和项 .这些结果扩展了 P-内射环的一些结果     

Noether环上的幂稳定自由模

设I是Noether环R的投射理想, I^m=Iⁿ, m≠n. 该文证明, 有限生成投射右R - 模幂稳定自由当且仅当(1) 存在环S使得I^|m-n|( S ( R且有限生成投射S - 模是幂稳定自由; (2) 有限生成投射右R/I^|m-n| - 模幂稳定自由.     

On Right Hereditary Rings and Dedekind Domains

ＯｎＲｉｇｈｔＨｅｒｅｄｉｔａｒｙＲｉｎｇｓａｎｄＤｅｄｅｋｉｎｄＤｏｍａｉｎｓＬｉｕＺｈｏｎｇｋｕｉ（刘仲奎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｗｅｓｔＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｚｈｏｕ，７３００７０）Ａｂｓ...     

关于基本可数生成子模的扩张性

称左R-模M是ecg-扩张模,如果M的任意基本可数生成子模是M的直和因子的基本子模.在研究了ecg-扩张模的基本性质的基础上,本文证明了对于非奇异环R,所有左R-模是ecg-扩张模当且仅当所有左R-模是扩张模.同时我们还用ecg-拟连续模刻画了Noether环和Artin半单环.     

广义逆多项式模的co-Hopf性质

设R是结合环(可以没有单位元),(S,≤)是严格全序幺半群,序≤是Artin的且对任意s∈S,有0≤s,则对任意具有性质(F)的左R-模M,[MS,≤]是co-Hopf左[[RS,≤]]一模当且仅当M是co-Hopf左R-模.     

On the existence of covers by injective modules relative to a torsion theory

Let R be a ring with identity. In this note we study covers of left R-modules by r-injectives left R-modules, where r is a hereditary torsion theory defined in the category of all left R-modules and all R-morphisms. When R is an artinian commutative ring, a complete answer about the existence of such covers for every R-module is given. In case that T is a centrally splitting torsion theory, we can characterize those T for which every left R-module has a T-injective cover. Also we analyze R-modules such that the injective and the T-injective cover are the same. At the end of this note we relate the concepts of colocalization and cover     

相对n-FP-内射模

给出了n-FP-内射模的定义,M为左R-模,如果对任意的左R-模N有Ext1(N,M)=0,则称M为n-FP-内射模,作为应用,给出了n-FP-内射模的一些等价条件.