H. Kose

activity

20132024

most citedRings in which every nilpotent is central

7 citations · 15 across the 13 of their papers we have counts for

collaborators

13 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

Strongly Rad-clean Matrices over Commutative Local Rings

Huanyin Chen, Handan Kose, Yosum Kurtulmaz

An element $a \in R$ is provided that there exists an idempotent $e \in R$ such that $a - e \in U (R), a e = e a$ and $e a e \in J (e R e)$ . In this article, we investigate strongly rad-clean matr…

math.RA2021

Perturbation for group inverse in a Banach algebra

Dayong Liu, Tugce Pekacar Calci, Handan Kose +1

We present new additive results for the group inverse in a Banach algebra under certain perturbations. The upper bound of $∥ (a + b)^{#} - a^{d} ∥$ is thereby given. These extend the ma…

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.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.RA2014

Factorizations of Matrices Over Projective-free Rings

H. Chen, H. Kose, Y. Kurtulmaz

An element of a ring $R$ is called strongly $J^{#}$ -clean provided that it can be written as the sum of an idempotent and an element in $J^{#} (R)$ that commute. We characterize,…

math.RA2014

On feckly clean rings

H. Chen, H. Kose, Y. Kurtulmaz

A ring $R$ is feckly clean provided that for any $a \in R$ there exists an element $e \in R$ and a full element $u \in R$ such that $a = e + u, e R (1 - e) \subseteq J (R)$ . We prove that a rin…

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★ 1 cited

Strongly Clean Matrices over Commutative Rings

H. Chen, H. Kose, Y. Kurtulmaz

A commutative ring $R$ is projective free provided that every finitely generated $R$ -module is free. An element in a ring is strongly clean provided that it is the sum of an idempo…

math.RA2013★ 2 cited

Uniquely Strongly Clean Triangular Matrix Rings

H. Chen, O. Gurgun, H. Kose

A ring $R$ is uniquely (strongly) clean provided that for any $a \in R$ there exists a unique idempotent $e \in R (\in co mm (a))$ such that $a - e \in U (R)$ . Let $R$ be a uniquel…

math.RA2013★ 2 cited

On Perfectly Clean Rings

H. Chen, S. Halicioglu, H. Kose

An element $a$ of a ring $R$ is called perfectly clean if there exists an idempotent $e \in co m m^{2} (a)$ such that $a - e \in U (R)$ . A ring $R$ is perfectly clean in case every element i…

math.RA2013★ 1 cited

Strongly clean triangular matrix rings with endomorphisms

H. Chen, H. Kose, Y. Kurtulmaz

A ring $R$ is strongly clean provided that every element in $R$ is the sum of an idempotent and a unit that commutate. Let $T_{n} (R, σ)$ be the skew triangular matrix ring over a loca…

math.RA2013

The strong $P$ -cleanness over rings

Huanyin Chen, H. Kose, Y. Kurtulmaz

An element of a ring $R$ is strongly $P$ -clean provided that it can be written as the sum of an idempotent and a strongly nilpotent element that commute. A ring $R$ is strongly $P$ …

e-Reduced rings in terms of the Zhou radical

Strongly Rad-clean Matrices over Commutative Local Rings

Perturbation for group inverse in a Banach algebra

Reversible ring property via idempotent elements

Reflexivity of Rings via Nilpotent Elements

Factorizations of Matrices Over Projective-free Rings

On feckly clean rings

Rings in which every nilpotent is central

Strongly Clean Matrices over Commutative Rings

Uniquely Strongly Clean Triangular Matrix Rings

On Perfectly Clean Rings

Strongly clean triangular matrix rings with endomorphisms

The strong P-cleanness over rings

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

The strong $P$ -cleanness over rings