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DERIVATIONS ON SUBTRACTION ALGEBRAS
Ozturk, Mehmet Ali,Ceven, Yilmaz Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.4
In this paper, we introduce the notions of a derivation and a generalized derivation determined by a derivation for a complicated subtraction algebra. We give some related properties and equivalent conditions which derivations hold.
Soft $\Gamma$-rings and idealistic soft $\Gamma$-rings
Mehmet Ali Ozturk,Ebubekir Inan 원광대학교 기초자연과학연구소 2011 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.1 No.1
Soft set theory has a rich potential for applications in several directions. In this paper, we introduce soft $\Gamma$-rings, soft ideals, and idealistic soft $\Gamma$-rings. We study some of their basic properties and give several illustrative examples.
MODULES OVER THE GENERALIZED CENTROID OF SEMI-PRIME GAMMA RINGS
Ozturk, Mehmet Ali,Yazarli, Hasret Korean Mathematical Society 2007 대한수학회보 Vol.44 No.2
The aim of this paper is to introduce modules over the generalized of a semi-prime ${\Gamma}$-ring
ON THE CENTROID OF THE PRIME GAMMA RINGS
Ozturk, Mehmet-Ali,Jun, Y.B. Korean Mathematical Society 2000 대한수학회논문집 Vol.15 No.3
We define and study the extended centroid of a prime $\Gamma$-ring.
REGULARITY OF THE GENERALIZED CENTROID OF SEMI-PRIME GAMMA RINGS
Ali Ozturk, Mehmet,Jun, Young-Bae Korean Mathematical Society 2004 대한수학회논문집 Vol.19 No.2
The aim of this note is to study properties of the generalized centroid of the semi-prime gamma rings. Main results are the following theorems: (1) Let M be a semi-prime $\Gamma$-ring and Q a quotient $\Gamma$-ring of M. If W is a non-zero submodule of the right (left) M-module Q, then $W\Gamma$W $\neq 0. Furthermore Q is a semi-prime $\Gamma$-ring. (2) Let M be a semi-prime $\Gamma$-ring and $C_{{Gamma}$ the generalized centroid of M. Then $C_{\Gamma}$ is a regular $\Gamma$-ring. (3) Let M be a semi-prime $\Gamma$-ring and $C_{\gamma}$ the extended centroid of M. If $C_{\gamma}$ is a $\Gamma$-field, then the $\Gamma$-ring M is a prime $\Gamma$-ring.
GENERALIZED DERIVATIONS OF BCI-ALGEBRAS
Ozturk, Mehmet Ali,Ceven, Yilmaz,Jun, Young-Bae The Honam Mathematical Society 2009 호남수학학술지 Vol.31 No.4
The notion of generalized derivations of a BCI-algebra is introduced, and some related properties are investigated. Also, the concept of a torsion free BCI-algebra is introduced and some properties are discussed.
Semiring on weak nearness approximation spaces
Mehmet Ali Ozturk 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.15 No.3
In this paper, our aim is to define the nearness semirings and to deal with their basic properties. Afterwards, we will study some properties of nearness semirings and ideals.
Mehmet Ali Ozturk,Ebubekir Inan 원광대학교 기초자연과학연구소 2019 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.17 No.2
In this paper, we consider the problem of how to establish algebraic structures on nearness approximation spaces. Essentially, our approach is to define the nearness ring, nearness ideal and nearness ring of all weak cosets by considering new operations on the set of all weak cosets. Afterwards, our aim is to study homomorphism on nearness approximation spaces, and to investigate some properties of nearness rings and ideals.
ON GENERALIZED SYMMETRIC BI-DERIVATIONS IN PRIME RINGS
Ozturk, M. Ali,Sapanci, Mehmet The Youngnam Mathematical Society Korea 1999 East Asian mathematical journal Vol.15 No.2
After the derivation was defined in [19] by Posner a lot of researchers studied the derivations in ring theory in different manners such as in [2], [4], [5], ..., etc. Furthermore, many researches followed the definition of the generalized derivation([3], [6], [7], ..., etc.). Finally, Maksa defined a symmetric bi-derivation and many researches have been done in ring theory by using this definition. In this work, defining a symmetric bi-$\alpha$-derivation, we study the mentioned researches above in the light of this new concept.