Now showing items 1-10 of 10

• Almost unit-clean rings ﻿

A ring R is almost unit-clean provided that every element in R is equivalent to the sum of an idempotent and a regular element. We investigate conditions under which a ring is almost unit-clean. We prove that every ring ...
• Duo property for rings by the quasinilpotent perspective ﻿

(Vasyl Stefanyk Precarpathian National University, 2021-03-16)
In this paper, we focus on the duo ring property via quasinilpotent elements, which gives anew kind of generalizations of commutativity. We call this kind of ringsqnil-duo. Firstly, someproperties of quasinilpotents in a ...
• Local comparability of exchange ideals ﻿

(Hacettepe University, 2019)
An exchange ideal I of a ring R is locally comparable if for every regular x ∈ I there exists a right or left invertible u ∈ 1+I such that x = xux. We prove that every matrix extension of an exchange locally comparable ...
• A nil approach to symmetricity of rings ﻿

We introduce a weakly symmetric ring which is a generalization of a symmetric ring and a strengthening of both a GWS ring and a weakly reversible ring, and investigate properties of the class of this kind of rings. A ring ...
• On π-Morphic modules ﻿

(Hacettepe University, Department of Mathematics, 2013)
Let R be an arbitrary ring with identity and M be a right R-module with S = End(MR). Let f ∈ S. f is called π-morphic if M/f n(M) ∼=rM(fn) for some positive integer n. A module M is called π-morphic if every f ∈ S is ...
• Reflexivity of rings via nilpotent elements ﻿

(Union Matematica Argentina, 2020)
An ideal I of a ring R is called left N-reflexive if for any a ∈ nil(R) and b ∈ R, aRb ⊆ I implies bRa ⊆ I, where nil(R) is the set of all nilpotent elements of R. The ring R is called left N-reflexive if the zero ideal ...
• Rings having normality in terms of the Jacobson radical ﻿

(Springer, 2020)
A ring R is defined to be J-normal if for any a,r∈Ra,r∈R and idempotent e∈Re∈R, ae=0ae=0 implies Rera⊆J(R)Rera⊆J(R), where J(R) is the Jacobson radical of R. The class of J-normal rings lies between the classes of weakly ...
• Rings in which elements are a sum of a central and a unit element ﻿

(The Belgian Mathematical Society, 2019)
In this paper we introduce a new class of rings whose elements are a sum of a central and a unit element, namely a ring RR is called CUCU if each element a∈Ra∈R has a decomposition a=c+ua=c+u where cc is central and uu is ...
• Semicommutativity of amalgamated rings ﻿

(Journal of Mathematical Research with Applications, 2018)
In this paper, we study some cases when an amalgamated construction A ◃▹f I of a ring A along an ideal I of a ring B with respect to a ring homomorphism f from A to B, is prime, semiprime, semicommutative, nil-semicommutative ...
• Structure theory of central simple ℤd-graded algebras ﻿

(TÜBİTAK, 2012)
This paper investigates the structure theory of ℤd- central simple graded algebras and gives the complete decomposition into building block algebras. The results are also applied to generalized Clifford algebras, which are ...