Related papers: Rings whose proper factors are right perfect
We answer in negative two of questions posed in [4]. We also establish a new characterization of semiprime left Goldie rings by showing that a semiprime ring R is left Goldie iff it is regular left fusible and has finite left Goldie…
Our aim is to study certain algebraic properties of the ring $C(X)_\mathcal{P}$ of real-valued functions on $X$ whose closure of discontinuity set is in an ideal of closed sets. We characterize $\mathcal{P}P$-spaces using $z$-ideals and…
In a paper on the taxonomy of 2-primal rings, examples of various types of rings that are related to commutativity such as reduced, symmetric, duo, reversible and PS~I were given in order to show that the ring class inclusions were strict.…
Let $R$ be a commutative ring with identity. In this paper, we introduce the concept of quasi $J$-ideal which is a generalization of $J$-ideal. A proper ideal of $R$ is called a quasi $J$-ideal if its radical is a $J$-ideal. Many…
In this paper we study the probability that the commutator of a randomly chosen pair of elements, one from a subring of a finite ring and other from the ring itself equals to a given element of the ring.
We extend to one dimensional quotients the result of A. Conca and S. Murai on the convexity of the regularity of Koszul cycles. By providing a relation between the regularity of Koszul cycles and Koszul homologies we prove a sharp…
The Bernstein-Sato polynomial is an important invariant of an element or an ideal in a polynomial ring or power series ring of characteristic zero, with interesting connections to various algebraic and topological aspects of the…
A ring is called a commutator ring if every element is a sum of additive commutators. In this paper we give examples of such rings. In particular, we show that given any ring R, a right R-module N, and a set X, End_R(\bigoplus_X N) and…
We study integrality over rings (all commutative in this paper) and over ideal semifiltrations (a generalization of integrality over ideals). We begin by reproving classical results, such as a version of the "faithful module" criterion for…
We discuss when the Rat functor associated to a coring satisfying the left $\alpha$-condition is exact. We study the category of comodules over a semiperfect coring. We characterize semiperfect corings over artinian rings and over qF-rings.
We prove that the finite generation of adjoint rings proved in [Cascini and Lazi\'c] implies all the foundational results of the Minimal Model Program: the Rationality, Cone and Contraction theorems, the existence of flips, and termination…
An element in a ring $R$ is called clear if it is the sum of unit-regular element and unit. An associative ring is clear if every its element is clear. In this paper we defined clear rings and extended many results to wider class. Finally,…
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…
A description of right (left) quasi-duo Z-graded rings is given. It shows, in particular, that a strongly Z-graded ring is left quasi-duo if and only if it is right quasi-duo. This gives a partial answer to a problem posed by Dugas and Lam…
Goldie's Theorem (1960), which is one of the most important results in Ring Theory, is a criterion for a ring to have a semisimple left quotient ring. The aim of the paper is to give four new criteria (using a completely different approach…
Gradient Ricci almost solitons were introduced by Pigola, Rigoli, Rimoldi and Setti. They are defined as solitons except that the metric coefficient is required to be a smooth function rather than a constant. It is shown that any almost…
The notion of clean rings and 2-good rings have many variations, and have been widely studied. We provide a few results about two new variations of these concepts and discuss the theory that ties these variations to objects and properties…
We show that there exists a complete local Noetherian normal domain of prime characteristic whose perfection is a non-coherent GCD domain, answering a question of Patankar in the negative concerning characterizations of $F$-coherent rings.…
Inspired by a question raised by Eisenbud-Musta\c{t}\u{a}-Stillman regarding the injectivity of maps from ${\rm Ext}$ modules to local cohomology modules and the work by the third author with Pham, we introduce a class of rings which we…
Let $f : A \rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we give a characterization of zero divisors of the amalgamation which is a generalization of Maimani's and Yassemi's work (see \cite{y}). Also, we…