Related papers: Rings Which Are Essential over Their Centers
Non-commutative Henselian rings are defined and it is shown that a local ring which is complete and separated in the topology defined by its maximal ideal is Henselian provided that it is almost commutative.
The goal of this article is to propose and examine the notion of graded classical weakly prime submodules over non-commutative graded rings which is a generalization of the concept of graded classical weakly prime submodules over…
We study the ring extensions R \subseteq T having the same set of prime ideals provided Nil(R) is a divided prime ideal. Some conditions are given under which no such T exist properly containing R. Using idealization theory, the examples…
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…
One of the main results of this paper is the characterization of the rings over which all modules are strongly Gorenstein projective. We show that these kinds of rings are very particular cases of the well-known quasi-Frobenius rings. We…
It follows from a recent paper by Ding and Wang that any ring which is generalized supplemented as left module over itself is semiperfect. The purpose of this note is to show that Ding and Wang's claim is not true and that the class of…
Let $R$ be a commutative ring with identity. For an $R$-module $M$, the notion of strongly prime submodule of $M$ is defined. It is shown that this notion of prime submodule inherits most of the essential properties of the usual notion of…
In this paper we introduce the concept of inessential element of a standard basis of I, where I is any homogeneous ideal of a polynomial ring. An inessential element is, roughly speaking, a form of the basis whose omission produces an ideal…
We introduce the notion of 'centre' for pomonoid-graded strong monads which generalizes some previous work that describes the centre of (not graded) strong monads. We show that, whenever the centre exists, this determines a pomonoid-graded…
In this paper, we introduce a strong property $(A)$ and we study the transfer of property $(A)$ and strong property $(A)$ in trivial ring extensions and amalgamated duplication of a ring along an ideal. We also exhibit a class of rings…
The main goal of this article is to introduce the concept of $EM-G-$graded rings. This concept is an extension of the notion of $EM-$rings. Let $G$ be a group and $R$ be a $G-$graded commutative ring. The $G-$gradation of $R$ can be…
We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.
We define the concepts of weakly precious and precious rings which generalize the notions of weakly clean and nil-clean rings. We obtain some fundamental properties of these rings. We also obtain certain subclasses of such rings and then…
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…
Our goal is to determine when the trivial extensions of commutative rings by modules are Cohen-Macaulay in the sense of Hamilton and Marley. For this purpose, we provide a generalization of the concept of Cohen-Macaulayness of rings to…
We investigate ideal-semisimple and congruence-semisimple semirings. We give several new characterizations of such semirings using e-projective and e-injective semimodules. We extend several characterizations of semisimple rings to (not…
In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…
In this paper, we compute the number of distinct centralizers of some classes of finite rings. We then characterize all finite rings with $n$ distinct centralizers for any positive integer $n \leq 5$. Further we give some connections…
For a ring endomirphism, we introduce the central skew Armendariz rings, which are a generalization of skew Armendariz rings and central Armendariz rings, and investigate their properties.
In the present paper, as a generalization of the classical periodic rings, we explore those rings whose elements are additively generated by two (or more) periodic elements by calling them additively periodic. We prove that, in some major…