Related papers: On 2-absorbing submodules and their Amalgamations

We use the concept of 2-absorbing ideal introduced by Badawi to study those commutative rings in which every proper ideal is a product of 2-absorbing ideals (we call them TAF-rings). Any TAF-ring has dimension at most one and the local…

Researchers introduced the notion of j-Artinian rings in [3] and obtained significant results concerning this new class of rings. Motivated by their definition and findings, we extend the study to modules by introducing the concept of…

Let $R$ be a commutative ring with identity. In this paper, we introduce the concept of weakly $1$-absorbing prime ideals which is a generalization of weakly prime ideals. A proper ideal $I$ of $R$ is called weakly $1$-absorbing prime if…

In this paper, we will introduce two generalizations of second submodules of a module over a commutative ring and explore some basic properties of these classes of modules.

Let $R$ be a commutative ring with identity, $S$ a multiplicatively closed subset of $R$, and $M$ be an $R$-module. In this paper, we study and investigate some properties of $S$-primary submodules of $M$. Among the other results, it is…

Let $R$ be a commutative ring with $1\neq 0$ and $n$ be a fixed positive integer. A proper ideal $I$ of $R$ is said to be an \textit{$n$-OA ideal} if whenever $a_1a_2\cdots a_{n+1}\in I$ for some nonunits $a_1,a_2,\ldots,a_{n+1}\in R$, then…

For commutative rings with identity, we introduce and study the concept of semi $r$-ideals which is a kind of generalization of both $r$-ideals and semiprime ideals. A proper ideal $I$ of a commutative ring $R$ is called semi $r$-ideal if…

Let R be a commutative ring with identity. The concept of second submodule of an R-module (as a dual notion of prime submodules) was introduced and studied by S.Yassemi in 2001. This notion has obtained a great attention by many authors and…

Let R be a commutative ring with identity. In this paper, we introduce the concept 1-absrbing primary ideal of R.

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…

Summand absorbing submodules are common in modules over (additively) idempotent semirings, for example, in tropical algebra. A submodule $W$ of $V$ is summand absorbing, if $x + y \in W$ implies $x \in W, \; y \in W $ for any $x, y \in V$.…

Let $G$ be a group, $R$ be a $G$-graded commutative ring with nonzero unity and $GI(R)$ be the set of all graded ideals of $R$. Suppose that $\phi:GI(R)\rightarrow GI(R)\cup\{\emptyset\}$ is a function. In this article, we introduce and…

In this paper, we characterize an amalgamated duplication of a ring $R$ along a proper ideal $I$, $R\bowtie I$, which is quasi-Frobenius.

We introduce a general notion of depth two for ring homomorphism N --> M, and derive Morita equivalence of the step one and three centralizers, R = C_M(N) and C = End_{N-M}(M \o_N M), via dual bimodules and step two centralizers A =…

Let $M$ be a non-zero module over an associative (not necessarily commutative) ring. In this paper, we investigate the so-called \emph{second} and \emph{coprime} submodules of $M.$ Moreover, we topologize the spectrum $%…

A famous result due to L. S. Levy provides a classification of all finitely generated indecomposable modules over Dedekind-like rings. This motivates us to outline an approach to the classification of indecomposable pseudo-absorbing primary…

In this paper we prove that if $R$ is a commutative refinement ring and $M$, $N$ are two $R$-modules then, $M\cong N$ if and only if for every maximal ideal $m$ of $R$, $M_m\cong N_m$. We prove if $R$ is a refinement ring, then every…

This article is concerned with homological properties of local or graded rings whose defining relations are monomials on some regular sequence. The main result of the article positively answers a question of Avramov for such a ring $R$.…

Similar to the idea of relative projectivity, we introduce the notion of relative subprojectivity, which is an alternative way to measure the projectivity of a module. Given modules $M$ and $N$, $M$ is said to be {\em $N$-subprojective} if…

A module $M$ is called an automorphism-invariant module if every isomorphism between two essential submodules of $M$ extends to an automorphism of $M$. This paper introduces the notion of dual of such modules. We call a module $M$ to be a…