内射余分解类与投射分解类

令是直和与直和项封闭的右R-模类.本文讨论了关于内射余分解类与投射分解类的左(右)-维数和左正合函子之间的关系,并由此得到一些应用.     

Flat covers and cotorsion envelopes of sheaves

In this paper we prove that any sheaf of modules over any topological space (in fact, any -module where is a sheaf of rings on the topological space) has a flat cover and a cotorsion envelope. This result is very useful, as we shall explain later in the introduction, in order to compute cohomology, due to the fact that the category of sheaves ( -modules) does not have in general enough projectives.

     

$\mathcal{F}$-Perfect Rings and Modules

Let $R$ be a ring, and let $(\mathcal{F}, C)$ be a cotorsion theory. In this article, the notion of $\mathcal{F}$-perfect rings is introduced as a nontrial generalization of perfect rings and A-perfect rings. A ring $R$ is said to be right $\mathcal{F}$-perfect if $F$ is projective relative to $R$ for any $F ∈ \mathcal{F}$. We give some characterizations of $\mathcal{F}$-perfect rings. For example, we show that a ring $R$ is right $\mathcal{F}$-perfect if and only if $\mathcal{F}$-covers of finitely generated modules are projective. Moreover, we define $\mathcal{F}$-perfect modules and investigate some properties of them.     

关于(m,n)-凝聚模与预包络

In this paper,let m,n be two fixed positive integers and M be a right R-module,we define (m,n)-M-flat modules and (m,n)-coherent modules.A right R-module F is called (m,n) M-flat if every homomorphism from an (n,m)-presented right R-module into F factors through a module in addM.A left S-module M is called an (m,n)-coherent module if MR is finitely presented,and for any (n,m)-presented right R-module K,Horn(K,M) is a finitely generated left S-module,where S = End(MR).We mainly characterize (m,n)-coherent modules in terms of preenvelopes (which are monomorphism or epimorphism) of modules.Some properties of (m,n)-coherent rings and coherent rings are obtained as corollaries.     

相对平坦模的$\aleph$-积

设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中$0\leq A相似文献   

On slightly P-coherent rings

A ring R is called left slightly P-coherent if C is P-injective, for every left R-module exact sequence 0→A→B→C→0 with A and B P-injective. The properties of slightly P-coherent rings and several examples are studied to show that left slightly P-coherent rings fall in between left P-coherent rings and left strongly P-coherent rings. In terms of some derived functors, some homological dimensions over these rings are investigated. As applications, some new characterizations of p.p.rings are given.     

Modules over serial rings

This paper continues the study of Noetherian serial rings. General theorems describing the structure of such rings are proved. In particular, some results concerning π-projective and π-injective modules over serial rings are obtained. Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 880–892 June, 1999.     

Almost-Perfect Rings and Modules

Following [1 Amini , A. , Ershad , M. , Sharif , H. ( 2008 ). Rings over which flat covers of finitely generated modules are projective . Comm. Algebra 36 : 2862 – 2871 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]], a ring R is called right almost-perfect if every flat right R-module is projective relative to R. In this article, we continue the study of these rings and will find some new characterizations of them in terms of decompositions of flat modules. Also we show that a ring R is right almost-perfect if and only if every right ideal of R is a cotorsion module. Furthermore, we prove that over a right almost-perfect ring, every flat module with superfluous radical is projective. Moreover, we define almost-perfect modules and investigate some properties of them.