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

Following our previous work about quasi-projective dimension, in this paper, we introduce quasi-injective dimension as a generalization of injective dimension. We recover several well-known results about injective and Gorenstein-injective…

In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a…

We give a positive answer to a conjecture of Faith stating that a self-injective semiprimary ring is QF, for algebras which are at most countable dimensional modulo their Jacobson radical. As a consequence of the method used, we also give…

Let $R$ be a ring. In \cite{MD4} Mao and Ding defined an special class of $R$-modules that they called \( FP_n \)-projective $R$-modules. In this paper, we give some new characterizations of \( FP_n \)-projective $R$-modules and strong…

In this paper, we introduce the notion of uniformly S-pseudo-projective (u-S-pseudo-projective) modules as a generalization of u-S-projective modules. Let R be a ring and S a multiplicative subset of R. An R-module P is said to be…

We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…

In this paper, the notion of quasi-pseudo injectivity relative to a class of submodules, namely, quasi-pseudo principally injective has been studied. This notion is closed under direct summands. Several properties and characterizations have…

We denote by $\mathcal{W}$ the class of all pure projective modules. Present article we investigate $\mathcal{W}$-injective modules and these modules are defined via the vanishing of cohomology of pure projective modules. First we prove…

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…

The main purposes of this paper are to establish and exploit the result that, over a complete (Noetherian) local ring $R$ of prime characteristic for which the Frobenius homomorphism $f$ is finite, the appropriate restrictions of the…

In this note, we give several characterizations of left pure-semisimple in terms of the (pre)envelope, (pre)cover, direct limits, direct sums, inverse limits and direct products properties of pure-projective modules or pure-injective…

This paper studies the multiplicative ideal structure of commutative rings in which every finitely generated ideal is quasi-projective. Section 2 provides some preliminaries on quasi-projective modules over commutative rings. Section 3…

We apply the theory of cotorsion pairs to study closure properties of classes of modules with finite projective dimension with respect to direct limit operations and to filtrations. We also prove that if the ring is an order in an…

Let $R$ be a commutative ring. A quasi-Gorenstein $R$-module is an $R$-module such that the grade of the module and the projective dimension of the module are equal and the canonical module of the module is isomorphic to the module itself.…

This paper refines the relationship between centrally quasi-morphic and centrally morphic modules, correcting earlier equivalences and extending them to a broader module-theoretic framework. We prove that if a module \(M\) is…

We consider a finite acyclic quiver $\mathcal{Q}$ and a quasi-Frobenius ring $R$. We endow the category of quiver representations over $R$ with a model structure, whose homotopy category is equivalent to the stable category of…

For an arbitrary ring $R$, the largest strong left quotient ring $Q_l^s(R)$ of $R$ and the strong left localization radical $\glsR$ are introduced and their properties are studied in detail. In particular, it is proved that…

In this paper, we provide several new characterizations of the maximal right ring of quotients of a ring by using the relatively dense property. As a ring is embedded in its maximal right ring of quotients, we show that the endomorphism…

This paper introduces the notion of uniformly-S-pseudo-injective (u-S-pseudo-injective) modules as a generalization of u-S-injective modules. Let R be a ring and S a multiplicative subset of R. An R-module E is said to be…

Let $(R,\mathfrak{m},k)$ be a commutative Noetherian local ring. It is well-known that if $M$ is a finitely generated $R$-module of finite quasi-injective dimension, then $\operatorname{qid}_RM = \operatorname{depth} R$. In this paper, we…