Browsing by Author "Kose H."

Almost unit-clean rings

Chen H.; Kose H.; Kurtulmaz Y. (Editura Academiei Romane, 2019)

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 prove that every ring in which every zero-divisor is strongly ?-regular is almost unit-clean ...

Central CNZ rings

Kose H.; Harmancı A. (Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2018)

In this note, we introduce the concept of central CNZ rings, which is a generalization of CNZ rings [1]. A ring R is called central CNZ if for any a, b ?nil(R), ab = 0 implies that ba is central, where nil(R) is the set ...

A generalization of reduced rings

Kose H.; Ungor B.; Halicioglu S. (2012)

Let R be a ring with identity. We introduce a class of rings which is a generalization of reduced rings. A ring R is called central rigid if for any a, b ? R, a2b = 0 implies ab belongs to the center of R. Since every ...

A nil approach to symmetricity of rings

Ungor B.; Kose H.; Kurtulmaz H.Y.; Harmanci A. (Allahabad Mathematical Society, 2018)

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 ?-morphic modules

Harmanci A.; Kose H.; Kurtulmaz Y. (Hacettepe University, 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 ?-morphic if M/fn(M) ? ?M(fn) for some positive integer n. A module M is called ?-morphic if every f ? S is ...

Strongly clean triangular matrix rings with endomorphisms

Chen H.; Kose H.; Kurtulmaz Y. (Iranian Mathematical Society, 2015)

A ring R is strongly clean provided that every element in R is the sum of an idempotent and a unit that commutate. Let Tn(R; ?) be the skew triangular matrix ring over a local ring R where ? is an endomorphism of R. We ...