Browsing by Author "Kose, Handan"
Now showing items 112 of 12

ALMOST UNITCLEAN RINGS
Chen, Huanyin; Kose, Handan; Kurtulmaz, Yosum (EDITURA ACAD ROMANE, 2019)A ring R is almost unitclean 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 zerodivisor is strongly piregular is almost unitclean ... 
DECOMPOSITIONS OF 2 x 2 MATRICES OVER LOCAL RINGS
Chen, Huanyin; Halicioglu, Sait; Kose, Handan (PUBLICATIONS L INSTITUT MATHEMATIQUE MATEMATICKI, 2016)An element a of a ring R is called perfectly clean if there exists an idempotent e is an element of comm(2) (a) such that a  e is an element of U(R). A ring R is perfectly clean in case every element in R is perfectly ... 
EXTENSIONS OF STRONGLY piREGULAR RINGS
Chen, Huanyin; Kose, Handan; Kurtulmaz, Yosum (KOREAN MATHEMATICAL SOC, 2014)An ideal I of a ring R is strongly piregular if for any x is an element of I there exist n is an element of N and y is an element of I such that x(n) x(n+l)y. We prove that every strongly piregular ideal of a ring is a ... 
A GENERALIZATION OF REDUCED RINGS
Kose, Handan; Ungor, Burcu; Halicioglu, Sait (HACETTEPE UNIV, FAC SCI, 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 is an element of R, a(2)b = 0 implies ab belongs to the center of ... 
LOCAL COMPARABILITY OF EXCHANGE IDEALS
Kose, Handan; Kurtulmaz, Yosum; Chen, Huanyin (IEJAINT ELECTRONIC JOURNAL ALGEBRA, 2019)An exchange ideal I of a ring R is locally comparable if for every regular x is an element of I there exists a right or left invertible u is an element of 1 + I such that x = xux. We prove that every matrix extension of ... 
NILREFLEXIVE RINGS
Kose, Handan; Ungor, Burcu; Harmanci, Abdullah (ANKARA UNIV, FAC SCI, 2016)In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce nilreflexive rings. It is shown that the notion of nilreflexivity is a generalization ... 
On Medium *Clean Rings
Chen, Huanyin; Abdolyousefi, Marjan Sheibani; Kose, Handan (SPRINGER BASEL AG, 2019)A *ring R is called a medium *clean ring if every element in R is the sum or difference of an element in its Jacobson radical and a projection that commute. We prove that a ring R is medium *clean if and only if R is ... 
On Weak Symmetric Property of Rings
Harmanci, Abdullah; Kose, Handan; Ungor, Burcu (SOUTHEAST ASIAN MATHEMATICAL SOCSEAMS, 2018)A concept of a weak symmetric ring is defined by Ouyang and Chen, that is, a ring R is called weak symmetric if abc being nilpotent implies that acb is nilpotent for all a, b, c is an element of R. In this note we continue ... 
A perspective on amalgamated rings via symmetricity
Kose, Handan; Ungor, Burcu; Kurtulmaz, Yosum; Harmanci, Abdullah (AMER MATHEMATICAL SOC, 2019)In this paper, we deal with some versions of reversibility and symmetricity on amalgamated rings along an ideal. 
Semicommutativity of the rings relative to prime radical
Kose, Handan; Ungor, Burcu (CHARLES UNIV, 2015)In this paper, we introduce a new kind of rings that behave like semicommutative rings, but satisfy yet more known results. This kind of rings is called Psemicommutative. We prove that a ring R is Psemicommutative if and ... 
Strongly Clean Matrices Over Power Series
Chen, Huanyin; Kose, Handan; Kurtulmaz, Yosum (KYUNGPOOK NATL UNIV, DEPT MATHEMATICS, 2016)An n x n matrix A over a commutative ring is strongly clean provided that it can be written as the sum of an idempotent matrix and an invertible matrix that commute. Let R be an arbitrary commutative ring, and let A(x) is ... 
Uniquely strongly clean triangular matrices
Chen, Huanyin; Gurgun, Orhan; Kose, Handan (SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEYTUBITAK, 2015)A ring R is uniquely (strongly) clean provided that for any a is an element of R there exists a unique idempotent e is an element of R (e is an element of comm(a)) such that a e is an element of U(R). We prove, in this ...