Related papers: On the rings whose injective right modules are max…

This paper introduces and studies homological properties of new classes of modules, namely, the $\mathcal F_1$-flat modules and the $\mathcal F_1^{\fp}$-flat modules, where $\mathcal F_1$ stands for the class of right modules of flat…

Let $R$ be a commutative ring. An $R$-module $M$ is called a semi-regular $w$-flat module if $\Tor_1^R(R/I,M)$ is $\GV$-torsion for any finitely generated semi-regular ideal $I$. In this article, we show that the class of semi-regular…

We describe new classes of noetherian local rings $R$ whose finitely generated modules $M$ have the property that $Tor_i^R(M,M)=0$ for $i\gg 0$ implies that $M$ has finite projective dimension, or $Ext^i_R(M,M)=0$ for $i\gg 0$ implies that…

A ring $R$ is called right (small) dual if every (small) right ideal of $R$ is a right annihilator. Left (small) dual rings can be defined similarly. And a ring $R$ is called (small) dual if $R$ is left and right (small) dual. It is proved…

The categories of almost modules and almost algebras are introduced as a convenient setting for the development of Faltings' method of almost etale extensions. After some preliminaries of general "almost homological algebra" we construct…

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular. It is shown that there exists a class of modules which…

Assume that $R$ is a non-right perfect ring. Then there is a proper class of classes of (right $R$-) modules closed under transfinite extensions lying between the classes $\mathcal P _0$ of projective modules, and $\mathcal F _0$ of flat…

The main aim of this paper is to investigate rings over which all (finitely generated strongly) Gorenstein projective modules are projective. We consider this propriety under change of rings, and give various examples of rings with and…

Let R be a ring and n,k be two non-negative integers. As an extension of several known notions, we introduce and study (n,k)-weak cotorsion modules using the class of right R-modules with n-weak flat dimensions at most k. Various examples…

We introduce and investigate ss-injectivity as a generalization of both soc-injectivity and small injectivity. A module M is said to be ss-N-injective (where N is a module) if every R-homomorphism from a semisimple small submodule of N into…

Drinfeld recently suggested to replace projective modules by the flat Mittag--Leffler ones in the definition of an infinite dimensional vector bundle on a scheme $X$. Two questions arise: (1) What is the structure of the class $\mathcal D$…

Let $A$ be a ring with minimum condition on principal right ideals. It is proved that $\aleph_0$-distributive right (left) $A$-modules coincide with Artinian (Noetherian) right (left) $A$-modules. Rings, over which all right modules are…

We study rings $R$ for which whenever non-zero polynomials $f(x)$ and $g(x)$ satisfy $f(x)g(x)f(x)=0$, it implies that there is a non-zero element $r\in R$ such that $f(x)rf(x)=0$. We call such rings inner McCoy rings. We explore some…

This article introduces the notion of an NJ-reflexive ring and demonstrates that it is distinct from the concept of a reflexive ring. The class of NJ-reflexive rings contains the class of semicommutative rings, the class of left (right)…

Let $R$ be a commutative Noetherian local ring and let $M$ and $N$ be nonzero finitely generated $R$-modules. In this paper, we investigate how the finiteness of the homological dimension of Ext modules between $M$ and $N$ affects that of…

For a certain finite graph E, we consider the corresponding finite dimensional algebra A with radical square zero. An explicit compact generator for the homotopy category of acyclic complexes of injective (resp. projective) modules over A,…

In this paper we study (non-commutative) rings $R$ over which every finitely generated left module is a direct sum of cyclic modules (called left FGC-rings). The commutative case was a well-known problem studied and solved in 1970s by…

We study the existence of maximal ideals in preadditive categories defining an order $\preceq$ between objects, in such a way that if there do not exist maximal objects with respect to $\preceq$, then there is no maximal ideal in the…

Let R be a ring, X a class of R-modules and n>1 an integer. In this paper, via special finitely presented modules, we introduce the concepts of Gorenstein n-X-injective and n-X-flat modules. And aside, we obtain some equivalent properties…

In this paper we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a non-commutative ring called the skew polynomial rings $F[x;\theta ]$. After a brief description of the skew…