Related papers: A note on the localization of generalized injectiv…

Let $R$ be a ring, and $n$ a fixed nonnegative integer. An $R$-module $W$ is called $L_{n}$-injective if ${\rm Ext}_{R}^{1}(M,W)=0$ for any $R$-module $M$ with flat dimension at most $n$. In this paper, we prove first that…

In this paper, the notion of rings with uniformly S-w-Noetherian spectrum is introduced. Several characterizations of rings with uniformly S-w-Noetherian spectrum are given. Actually, we show that a ring R has uniformly S-w-Noetherian…

Let $R$ be a commutative Noetherian ring with identity and $C$ a semidualizing module for $R$. Let $\mathscr{P}_C(R)$ and $\mathscr{I}_C (R)$ denote, respectively, the classes of $C$-projective and $C$-injective $R$-modules. We show that…

We prove that $F$-injectivity localizes, descends under faithfully flat homomorphisms, and ascends under flat homomorphisms with Cohen-Macaulay and geometrically $F$-injective fibers, all for arbitrary Noetherian rings of prime…

Let A be a noncommutative noetherian with dualizing complex R. We study the multiplicities of indecomposable injectives in a minimal injective resolution of R. In particular when A is a Gorenstein ring we get information on minimal…

For a Noetherian regular ring $S$ and for a fixed ideal $J\subset S$, assume that the associated primes of local cohomology module $H^i_J(S)$ does not contain $p$ for some $i\geq 0$, and we call this as a property…

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? This note provides, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov…

Given a multiplicative subset $S$ in a commutative ring $R$, we consider $S$-weakly cotorsion and $S$-strongly flat $R$-modules, and show that all $R$-modules have $S$-strongly flat covers if and only if all flat $R$-modules are…

Suppose that $(\mathcal{F},\mathcal{M})$ is an injective structure of $R$-Mod such that the class $\mathcal{F}$ is closed for direct limits, then two modules in $\mathcal{M}$ are isomorphic if there are maps in $\mathcal{F}$ from each one…

A finitely generated module C over a commutative noetherian ring R is semidualizing if Hom_R(C,C) \cong R and Ext^i_R(C,C) = 0 for all i \geq 1. For certain local Cohen-Macaulay rings (R,m), we verify the equality of Hilbert-Samuel…

We study the structure of seminoetherian modules. Seminoetherian modules over non-primitive hereditary noetherian prime rings are completely described.

Let $R$ and $S$ be rings, $C= {}_SC_R$ a (faithfully) semidualizing bimodule, and $n$ a positive integer or $n=\infty$. In this paper, we introduce the concepts of $C$-$fp_n$-injective $R$-modules and $C$-$fp_n$-flat $S$-modules as a common…

We study injective hulls of simple modules over differential operator rings $R[\theta; d]$, providing necessary conditions under which these modules are locally Artinian. As a consequence we characterize Ore extensions of…

We introduce the notion of a severe right Ore set in the main as a tool to study universal localisations of rings but also to provide a short proof of P. M. Cohn's classification of homomorphisms from a ring to a division ring. We prove…

We show that if a graded submodule of a Noetherian module cannot be written as a proper intersection of graded submodules, then it cannot be written as a proper intersection of submodules at all. More generally, we show that a natural…

It is proven that each indecomposable injective module over a valuation domain $R$ is polyserial if and only if each maximal immediate extension $\widehat{R}$ of $R$ is of finite rank over the completion $\widetilde{R}$ of $R$ in the…

Let $G$ be an abelian group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper we will obtain some results concerning the graded generalized 2-absorbing submodules and their homogeneous…

A well-known result of K\"{o}the and Cohen-Kaplansky states that a commutative ring $R$ has the property that every $R$-module is a direct sum of cyclic modules if and only if $R$ is an Artinian principal ideal ring. This motivated us to…

For a left coherent ring A with every left ideal having a countable set of generators, we show that the coderived category of left A-modules is compactly generated by the bounded derived category of finitely presented left A-modules…

Let $\mathcal{X}$ be a class of $R$-modules. In this paper, we investigate \;$\mathcal{X}$-(f.g.)injective ((f.g.)projective) and DG-$\mathcal{X}$-injective (projective) complexes which are generalizations of injective (projective) and…