Related papers: Foxby equivalence relative to $C$-$fp_n$-injective…

Let $R$ be a commutative ring with a non-zero identity, $S$ be a multiplicatively closed subset of $R$ and $M$ be a unital $R$-module. In this paper, we define a submodule $N$ of $M$ with $(N:_{R}M)\cap S=\emptyset$ to be weakly $S$-primary…

In this paper, we are interested in a class of modules partaking in the hierarchy of injective and cotorsion modules, so-called Harmanci injective modules, which turn out by the motivation of relations among the concepts of injectivity,…

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…

In this paper, we introduce and study V- and CI-semirings---semirings all of whose simple and cyclic, respectively, semimodules are injective. We describe V-semirings for some classes of semirings and establish some fundamental properties…

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…

In this expository article, we will give an efficient functorial proof of the equivalence of various characterisations of purity in a finitely accessible additive category $\mathcal C$. The complications of the proofs for specific choices…

We investigate commutative Noetherian rings of prime characteristic such that the Frobenius functor applied to any injective module is again injective. We characterize the class of one-dimensional local rings with this property and show…

In this paper, we compare $(n,m)$-purities for different pairs of positive integers $(n,m)$. When $R$ is a commutative ring, these purities are not equivalent if $R$ doesn't satisfy the following property: there exists a positive integer…

The $C$-quasi-injective dimension is a recently introduced homological invariant that unifies and extends the notions of quasi-injective dimension and of injective dimension with respect to a semidualizing module, previously studied by…

In this paper, we introduce a new concept in Nil-semicommutative modules and present it as an extension of Nil-semicommutative rings to modules. We prove that the class of Nil-semicommutative modules is contained in the class of Weakly…

It is proven that the weak dimension of each FP-injective module over a chain ring which is either Archimedean or not semicoherent is less or equal to 2.

It is well-known that a class of all modules, which are torsion-free with respect to a set of ideals, is closed under injective envelopes. In this paper, we consider a kind of a dual to this statement - are the divisibility classes closed…

Let R be a commutative ring with unity and M be an R- module In this paper we introduce semi n- absorbing and (k, n)-closed submodules of modules over commutative rings, and investigate their basic properties.

This paper is concerned with S-co-m modules which are a generalization of co-m modules. In section 2, we introduce the S-small and S-essential submodules of a unitary $R$-module $M$ over a commutative ring $R$ with $1\neq 0$ such that S is…

Let $R$ be a $G$-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly graded rings and invertible graded rings, and we discuss the relations between these concepts and several properties of graded…

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 $R=k[x_1,..., x_n]$ be a polynomial ring over a field $k$ of characteristic $p>0,$ let $\m=(x_1,..., x_n)$ be the maximal ideal generated by the variables, let $^*E$ be the naturally graded injective hull of $R/\m$ and let $^*E(n)$ be…

Let $(R, \frak m)$ denote a local Cohen-Macaulay ring and $I$ a non-nilpotent ideal of $R$. The purpose of this article is to investigate Faltings' finiteness dimension $f_I(R)$ and equidimensionalness of certain homomorphic image of $R$.…

Recently, many authors have embraced the study of certain properties of modules such as projectivity, injectivity and flatness from an alternative point of view. Rather than saying a module has a certain property or not, each module is…

In this paper, we introduce and study the notion of strongly $\phi$-$w$-flat modules. The $\phi$-$w$-weak global dimension $\phi$-$w$-w.gl.dim$(R)$ of an NP-ring $R$ is also introduced and studied. We characterize $\phi$-\Prufer\…