Related papers: On S-Comultiplication Modules

Let R be a semiring. We say that a non-zero subsemimodule S of an R-semimodule M is second if for each a \in R, we have aS = S or aS = 0. The aim of this paper is to study the notion of second subsemimodules of semimodules over commutative…

This paper introduces the notion of co-modularity, to co-cluster observations of bipartite networks into co-communities. The task of co-clustering is to group together nodes of one type with nodes of another type, according to the…

Let R be a commutative ring with identity. A prime submodule P of an R-module M is called coprimely structured if, whenever P is coprime to each element of an arbitrary family of submodules of M, the intersection of the family is not…

Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. First, we introduce and study the $S$-projective dimensions and $S$-injective dimensions of $R$-modules, and then explore the $S$-global dimension…

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded classical and graded strongly classical 2-absorbing second submodules of graded…

We introduce a dual Zariski topology on the spectrum of fully coprime $R$-submodules of a given duo module $M$ over an associative (not necessarily commutative) ring $R$. This topology is defined in a way dual to that of defining the…

We study prime ideals, prime modules, and associated primes of graded modules over rings $S$ graded by a unique product monoid. We consider two situations in detail: (a) the case where $S$ is strongly group-graded and (b) the case where $S$…

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring, $M$ a graded $R$-module and $A\subseteq h(R)$ a multiplicatively closed subset of $R$. In this paper, we introduce the concept of graded $A$-2-absorbing…

Let $R$ be a commutative ring and $S$ a multiplicative subset of $R$. A ring $R$ is called an $S$-Matlis ring if $pd_RR_S\leq 1$. In this note, we give some new characterizations of $S$-Matlis rings in terms of $S$-strongly flat modules,…

All rings are commutative, and all modules are unital. The purpose of this paper is to investigate the characterizations of weakly pseudo primary 2-absorbing sub-module in terms of some types of modules. We provide characterizations for the…

Let R be a commutative ring, M an R-module. In this paper, we will introduce the concept of n-pure submodules of M as a generalization of pure submodules and obtain some related results.

Let $R$ be a commutative ring with identity, and let $S$ be a multiplicative subset of $R$. In this paper, we introduce the notion of $S$-injective modules as a weak version of injective modules. Among other results, we provide an…

Let R be a commutative ring with identity and M be an R-module. A proper ideal I of R is said to be a $z^\circ$-ideal if for each $a \in I$ the intersection of all minimal prime ideals containing a is contained in I. The purpose of this…

In this work, we introduce the notion of $S$-1-absorbing primary submodule as an extension of 1-absorbing primary submodule. Let $S$ be a multiplicatively closed subset of a ring $R$ and $M$ be an $R$-module. A submodule $N$ of $M$ with…

In this note we introduce and investigate the concepts of dual entwining structures and dual entwined modules. This generalizes the concepts of dual Doi-Koppinen structures and dual Doi-Koppinen modules introduced (in the infinite case over…

All rings considered are commutative. In this article we introduce and study two notions of modules which are stronger than CS modules, namely weakly IN modules and strongly CS modules. Our main aim is to characterize when a trivial…

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. The aim of this paper is to extend the notion of quasi $J$-ideals of commutative rings to quasi $J$-submodules of modules. We call a proper submodule $N$ of $M$ a…

Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we introduce and study the notions of $S$-pure $S$-exact sequences and $S$-absolutely pure modules which extend the classical notions of pure…

The purpose of this article is to introduce the graded classical S-primary submodules which are extensions of graded classical primary submodules. We state that P is a graded classical S-primary submodule of R-module M if there exists $s\in…

Based upon properties of ordinal length, we introduce a new class of modules, the binary modules, and study their endomorphism ring. The nilpotent endomorphisms form a two-sided ideal, and after factoring this out, we get a commutative…