Related papers: Commutativity criteria for prime rings with involu…
Let $R$ be a ring and $P$ a prime ideal of $R.$ In this paper, we establish some commutativity criteria for the factor ring $R/P$ in terms of derivations of $R$ satisfying some algebraic identities involving a new kind of involution in…
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…
In this paper we review and study $R$-modules $M$ for which $S = End_R(M)$ is commutative. For this, we define the concept of center of modules which is a natural generalization of the center of rings. The properties of center of modules,…
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…
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…
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime Ideal Principle" that gives a uniform method of proving such facts, generalizing the…
In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties…
The aim of this paper is to investigate properties of endo-prime and endo-coprime modules which are generalizations of prime and simple rings, respectively. Various properties of endo-coprime modules are obtained. Duality-like connections…
We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of a discrete data determined by the images of parameters. In similar terms, we…
Let $R$ be a unital ring with involution.In this paper, several new necessary and sufficient conditions for the existence of the Moore-Penrose inverse of an element in a ring $R$ are given.In addition, the formulae of the Moore-Penrose…
In this study, we introduce the concept of "uniformly 2-absorbing primary ideals" of commutative rings, which imposes a certain boundedness condition on the usual notion of 2-absorbing primary ideals of commutative rings. Then we…
The notion of ring endomorphisms having large images is introduced. Among others, injectivity and surjectivity of such endomorphisms are studied. It is proved, in particular, that an endomorphism S of a prime one-sided noetherian ring R is…
Inspired by methods in prime characteristic in commutative algebra, we introduce and study combinatorial invariants of seminormal monoids. We relate such numbers with the singularities and homological invariants of the semigroup ring…
In the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are…
The main purpose of this paper is to investigate prime, primary, and maximal ideals of semirings. The localization and primary decomposition of ideals in semirings are also studied.
Unique factorization fails in many rings and monoids, but divisor and transfer homomorphisms provide tools to understand non-unique factorizations. In this expository article, we first explore these notions in the classical setting of…
In recent years, centrally essential rings have been intensively studied in ring theory. In particular, they find applications in homological algebra, group rings, and the structural theory of rings. The class of essentially central rings…
The aim of this article is to introduce the concept of centrally-extended Jordan endomorphisms and proving that if $R$ is a non-commutative prime ring of characteristic not two, and $G$ is a CE- Jordan epimorphism such that $[G(x), x] \in…
In this paper, we introduce multiplicative semiderivation and we investigate the commutativity of semiprime rings satisfying certain conditions and identities involving multiplicative semiderivations on a nonzero ideal I of a ring R.
In this paper, we introduce and study two new classes of commutative rings, namely semi transitional rings and transitional rings, which extend several classical ideas arising from rings of continuous functions and their variants. A general…