B. Ungor

activity

20122024

most citedRings in which every nilpotent is central

7 citations · 16 across the 11 of their papers we have counts for

collaborators

12 papers

math.RA2024

$e$ -Reduced rings in terms of the Zhou radical

Handan Kose, Burcu Ungor, Abdullah Harmanci

Let $R$ be a ring, $e$ an idempotent of $R$ and $δ (R)$ denote the intersection of all essential maximal right ideals of $R$ which is called Zhou radical. In this paper, the Zhou ra…

math.RA2022

The Natural partial order on modules

Tugba Pakel, Tugce Pekacar Calci, Sait Halicioglu +2

The Mitsch order is already known as a natural partial order for semigroups and rings. The purpose of this paper is to further study of the Mitsch order on modules by investigating…

math.RA2021★ 2 cited

Duo property for rings by the quasinilpotent perspective

Abdullah Harmanci, Yosum Kurtulmaz, Burcu Ungor

In this paper, we focus on the duo ring property via quasinilpotent elements which gives a new kind of generalizations of commutativity. We call this kind of ring qnil-duo. Firstly…

math.RA2020

Reversible ring property via idempotent elements

Handan Kose, Burcu Ungor, Abdullah Harmanci

Regarding the question of how idempotent elements affect reversible property of rings, we study a version of reversibility depending on idempotents. In this perspective, we introdu…

math.RA2019★ 5 cited

Minus Partial Order in Regular Modules

Burcu Ungor, Sait Halicioglu, Abdullah Harmanci +1

The minus partial order is already known for sets of matrices over a field and bounded linear operators on arbitrary Hilbert spaces. Recently, this partial order has been studied o…

math.RA2019

Harmanci Injectivity of Modules

Burcu Ungor

In this paper, we are interested in a class of modules partaking in the hierarchy of injective and cotorsion modules, so-called Harmanci injective modules, which turn out by the mo…

math.RA2018

Prime Structures in a Morita Context

Mete Burak Calci, Sait Halicioglu, Abdullah Harmanci +1

In this paper, we study on the primeness and semiprimeness of a Morita context related to the rings and modules. Necessary and sufficient conditions are investigated for an ideal o…

math.RA2018★ 2 cited

Reflexivity of Rings via Nilpotent Elements

Abdullah Harmanci, Handan Kose, Yosum Kurtulmaz +1

An ideal $I$ of a ring $R$ is called left N-reflexive if for any $a \in$ nil $(R)$ , $b \in R$ , being $a R b \subseteq I$ implies $b R a \subseteq I$ where nil $(R)$ is the set of all nilpo…

math.RA2013★ 7 cited

Rings in which every nilpotent is central

Burcu Ungor, Sait Halicioglu, Handan Kose +1

In this paper, we introduce a class of rings in which every nilpotent element is central. This class of rings generalizes so-called reduced rings. A ring $R$ is called {\it central…

math.RA2013

Rickart Modules Relative to Goldie Torsion Theory

Burcu Ungor, Sait Halicioglu, Abdullah Harmanci

Let $R$ be an arbitrary ring with identity and $M$ a right $R$ -module with $S =$ End $_{R} (M)$ . Let $Z_{2} (M)$ be the second singular submodule of $M$ . In this paper, we define Goldie Ri…

math.RA2012

A Generalization of Rickart Modules

Burcu Ungor, Sait Halıcıoglu, Abdullah Harmanci

Let $R$ be an arbitrary ring with identity and $M$ a right $R$ -module with $S =$ End $_{R} (M)$ . In this paper we introduce $π$ -Rickart modules as a generalization of generalized right…