Related papers: Semi-regular flat modules over strong Pr\"{u}fer r…

Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. An $R$-module $M$ is said to be a uniformly $S$-Artinian ($u$-$S$-Artinian for abbreviation) module if there is $s\in S$ such that any descending chain of…

In this article, we introduce the notion of regular fusible modules. Let $R$ be a ring with an identity and $M$ an $R$-module. An element $0\neq m\in M$ is said to be regular fusible if there exists $r\in R$, a non zero-divisor of $M$, such…

Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…

In this paper we define and study quasipolar general rings (with or without identity) and extend many of the basic results to the wider class. We obtain some new characterizations of quasipolar and strongly $\pi$-regular elements by using…

It is known that every $R$-module has a flat precover. We show in the paper that every $R$-module has a Gorenstein flat precover.

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 an affine algebra over an algebraically closed field of characteristic $0$ with dim$(R)=n$. Let $P$ be a projective $A=R[T_1,\cdots,T_k]$-module of rank $n$ with determinant $L$. Suppose $I$ is an ideal of $A$ of height $n$ such…

In this paper, we investigate the question of when a $\phi$-ring is $\phi$-Pr\"ufer using two types of techniques: first, by analysing the lattice structure of the nonnil ideals of $\phi$-rings; and secondly, by considering content ideal…

Let $(R,\mathfrak{m},K)$ be an $F$-finite Noetherian local ring which has a canonical ideal $I \subsetneq R$. We prove that if $R$ is $S_2$ and $H^{d-1}_{\mathfrak{m}}(R/I)$ is a simple $R\{F\}$-module, then $R$ is a strongly $F$-regular…

The purpose of the present paper is to prove some properties of the strongly irreducible submodules in the arithmetical and Noetherian modules over a commutative ring. The relationship among the families of strongly irreducible submodules,…

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular. It is shown that there exists a class of modules which…

A module is said to be \textsf{distributive} if the lattice of its submodules is distributive. A direct sum of distributive modules is called a \textsf{semidistributive} module. In this paper we consider rings $A$ such that all right…

Let (R,m) be a noetherian local ring and let $\mathcal{C}$ be the class of all R-modules M which possess a reflexive submodule U such that M/U is finitely generated. For every R-module $M\in \mathcal{C}$ the canonical embedding $\varphi:…

We reconsider a classical theorem by Bican and El Bashir, which guarantees the existence of non-trivial relatively pure submodules in a module category over a ring with unit. Our aim is to generalize the theorem to module categories over…

For an $R$-module $M$, projective in $\sigma[M]$ and satisfying ascending chain condition (ACC) on left annihilators, we introduce the concept of Goldie module. We also use the concept of semiprime module defined by Raggi et. al. in…

In this paper we study and investigate concerning dependent elements of semiprime rings and prime rings R by using generalized derivation and derivation,when R admsit to satisfy some conditions,we give some results about that.

Let $R$ be a commutative ring with non-zero identity and $M$ be a unitary $R$-module. Let $\mathcal{S}(M)$ be the set of all submodules of $M$, and $\phi:\mathcal{S}(M)\to \mathcal{S}(M)\cup \{\emptyset\}$ be a function. We say that a…

We classify thick subcategories of the $\infty$-categories of perfect modules over ring spectra which arise as functions on even periodic derived stacks satisfying affineness and regularity conditions. For example, we show that the thick…

Let R be a ring (associative, with 1). A non-zero module M is said to be a Pruefer module provided there exists a surjective, locally nilpotent endomorphism with kernel of finite length. The aim of this note is construct Pruefer modules…

In this paper we give elementary conditions completely characterising when the theory of modules of a Pr\"ufer domain is decidable. Using these results, we show that the theory of modules of the ring of integer valued polynomials is…