Related papers: Modules with commutative endomorphism rings

Let $R$ be a commutative Noetherian ring and $M$ a finitely generated $R$-module. Under various hypotheses, it is proved that the center of $\mbox{End}_R(M)$ coincides with the endomorphism ring of the trace ideal of $M$. These results are…

Let $R$ be a commutative Noetherian local ring and $M$ a finitely generated $R$-module. We introduce a general form of the classically studied trace map that unifies several notions from the literature. We develop a theory around these…

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…

Let $R$ be a commutative Noetherian local ring. We study tensor products involving a finitely generated $R$-module $M$ through the natural action of its endomorphism ring. In particular, we study torsion properties of self tensor products…

Let $R$ be a local ring and let $M$ be a finitely generated $R$-module. Appealing to the natural left module structure of $M$ over its endomorphism ring and corresponding center $Z(\operatorname{End}_R(M))$, we study when various…

We study the construction and properties of modules whose endomorphism rings have a unique two-sided maximal ideal.

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and let M be an R-module. The aim of this paper is to introduce the notion of S-secondary submodules of M as a generalization of secondary submodules of…

The aim of this article is to investigate central-valued identities involving pairs of endomorphisms on prime rings equipped with an involution of the second kind. Extending the recent contributions of Mir et al. (2020) and Boua et al.…

Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module with $S =$ End$_R(M)$. In this paper we introduce dual $\pi$-Rickart modules as a generalization of $\pi$-regular rings as well as that of dual Rickart modules. The…

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduce and investigate the dual notion of morphic modules over a commutative ring.

Endomorphism rings of modules appear as the center of a ring, as the fix ring of ring with group action or as the subring of constants of a derivation. This note discusses the question whether certain *-prime modules (introduced by Bican et…

We describe the endomorphism rings in an additive category whose objects are right $R$-modules $M$ with a fixed chain of submodules $0=M^{(0)}\leq M^{(1)}\leq M^{(2)} \leq \dots \leq M^{(n)}=M$ and the behaviour of these objects as far as…

In this paper we study endomorphism rings of finite global dimension over not necessarily normal commutative rings. These objects have recently attracted attention as noncommutative (crepant) resolutions, or NC(C)Rs, of singularities. We…

We study the category $\operatorname{Morph}(\operatorname{Mod} R)$ whose objects are all morphisms between two right $R$-modules. The behavior of objects of $\operatorname{Morph}(\operatorname{Mod} R)$ whose endomorphism ring in…

In this paper, we are mainly interested in the two questions "which are the commutative rings on which every finitely presented modules is [Formula: see text]-periodic (respectively, [Formula: see text]-periodic)?". It is proved that these…

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…

Let R be a commutative ring with identity and M be an R-module. In this paper, we will introduce the concept of 2-irreducible (resp., strongly 2- irreducible) submodules of M as a generalization of irreducible (resp., strongly irreducible)…

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 $R$ 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 be a commutative ring with identity and S be a multiplicatively closed subset of R. In this article we introduce the concepts of S-coidempotent submodules and fully S-coidempotent R-modules as generalizations of coidempotent…