Related papers: On right $S$-Noetherian rings and $S$-Noetherian m…

A classification of multiplication modules over multiplication rings with finitely many minimal primes is obtained. A characterisation of multiplication rings with finitely many minimal primes is given via faithful, Noetherian, distributive…

Matlis showed that the injective hull of a simple module over a commutative Noetherian ring is Artinian. Many non-commutative Noetherian rings whose injective hulls of simple modules are locally Artinian have been extensively studied…

Let $R$ be a commutative (Noetherian) local ring of prime characteristic $p$ that is $F$-pure. This paper is concerned with comparison of three finite sets of radical ideals of $R$, one of which is only defined in the case when $R$ is…

In this paper, we study module theoretic definitions of the Baer and related ring concepts. We say a module is s.Baer if the right annihilator of a nonempty subset of the module is generated by an idempotent in the ring. We show that s.Baer…

Let $R$ be a commutative noetherian ring. The $n$-semidualizing modules of $R$ are generalizations of its semidualizing modules. We will prove some basic properties of $n$-semidualizing modules. Our main result and example shows that the…

We characterize the commutative rings whose ideals (resp. regular ideals) are products of radical ideals.

An $R$-module $M$ is called absolutely self pure if for any finitely generated left ideal of $R$ whose kernel is in the filter generated by the set of all left ideals $L$ of $R$ with $L \supseteq$ ann $(m)$ for some $m \in M$, any map from…

For several semirings S, two weighted finite automata with multiplicities in S are equivalent if and only if they can be connected by a chain of simulations. Such a semiring S is called "proper". It is known that the Boolean semiring, the…

Two left noetherian rings $R$ and $S$ are said to be {\it singularly equivalent} if their singularity categories are equivalent as triangulated categories. The aim of this paper is to give a necessary condition for two commutative…

Let $A$ be a ring with minimum condition on principal right ideals. It is proved that $\aleph_0$-distributive right (left) $A$-modules coincide with Artinian (Noetherian) right (left) $A$-modules. Rings, over which all right modules are…

A famous result due to I. M. Isaacs states that if a commutative ring $R$ has the property that every prime ideal is principal, then every ideal of $R$ is principal. This motivates ring theorists to study commutative rings for which every…

Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module of dimension $d$. If $R$ is a complete local ring and $M$ is finite, then attached prime ideals of $H^{d-1}_{I,J}(M)$ are computed by means of the…

Let A be a Noetherian ring and B be a finitely generated A-algebra. Denote by A' the integral closure of A in B. We give necessary and sufficient conditions for prime ideals to be in Ass_{A}(B/A') and Ass_{A'}(B/A') generalizing and…

We study prime ideals in skew power series rings $T:=R[[y;\tau,\delta]]$, for suitably conditioned right noetherian complete semilocal rings $R$, automorphisms $\tau$ of $R$, and $\tau$-derivations $\delta$ of $R$. These rings were…

In this paper, we investigate the notions of almost Noetherian rings and modules. In details, we give the Cohen type theorem, Eakin-Nagata type theorem, Kaplansky type Theorem and Hilbert basis theorem and some other rings constructions for…

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The aim of this paper is to introduce the notion of fully S-idempotent modules as a generalization of fully idempotent modules and investigate some…

Given a commutative Noetherian ring $R$ with total ring of fractions $Q(R)$, and a finitely generated $R$-submodule $M$ of $Q(R)$, we prove an equality between trace ideal, and certain annihilator of Ext and Tor of $M$. As a consequence, we…

In this paper we study commutative rings $R$ whose prime ideals are direct sums of cyclic modules. In the case $R$ is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it…

Let R be a commutative ring with identity and N(R) be the set of all nilpotent elements of R. The aim of this paper is to introduce and study the notion of nil-prime ideals as a generalization of prime ideals. We say that a proper ideal P…

Matlis duality for modules over commutative rings gives rise to the notion of Matlis reflexivity. It is shown that Matlis reflexive modules form a Krull-Schmidt category. For noetherian rings the absence of infinite direct sums is a…