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In this paper, the notion of generalized centroid is applied to hyperrings. We show that the generalized centroid C of a semiprime hyperring R is a regular hyperring. Also, we show that if C is a hyperfield, then R is a prime hyperring.

In this paper, we define the generalized q-Cesáro matrix by using generalized Cesáro matrix and q-Cesáro matrix. We investigate normality, self-adjointedness and Hilbert-Schmidt properties of generalized q-Cesáro matrices. [ABSTRACT FROM AUTHOR]

In this study, we define the generalized symmetric bi-derivation and its trace on MV-algebras and give its examples. We investigate some properties of generalized symmetric bi-derivation's trace. We introduce isotone generalized symmetric bi-derivation and bi-additive generalized symmetric bi-derivation. We show that if A is a linearly ordered MV-algebra, Γ is a bi-additive generalized symmetric bi-derivation on A related to symmetric bi-derivation D and γ is a trace of Γ, then γ = 0 or γ1 = 1 [ABSTRACT FROM AUTHOR]

In this study, we give definition of symmetric bi-derivation on bitonic algebras and investigate its properties. [ABSTRACT FROM AUTHOR]

In this study, we investigate the problem of how to define Γ -nearness semiring in the sense of Nobusawa theory which extends the notion of a nearness rings, nearness semirings and Γ -rings [N. Nobusawa, On a generalization of the ring theory, Osaka Journal of Mathematics1 (1964) 81–89; M. A. Öztürk, Semirings on weak nearness approximation spaces, Annals of Fuzzy Mathematics and Informatics15(3) (2018) 227–241; M. A. Öztürk and E. İnan, Nearness rings, Annals of Fuzzy Mathematics and Informatics17(2) (2019) 115–132]. Also, we introduce some properties of approximations and their algebraic structures. [ABSTRACT FROM AUTHOR]

In this paper, the notation of extended centroid is applied to hyperring. We show that the extended centroid C of a hyperring is a hyperfield. Also, we show that if a, b ∈ S such that axb = bxa for all x ∈ R, then there exists q ∈ C such that qa = b where R is a prime hyperring and S be the central closure of R. Finally we give some relations between the extended centroid and derivation in hyperring. [ABSTRACT FROM AUTHOR]

We define and study the generalized centroid of a semiprime semiring. Let R be a right multiplicatively cancellable semiprime semiring and C the generalized centroid of R, then C is semi-field. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some results concerning permuting triderivations and permuting generalized triderivations on prime and semiprime rings which partially extend some results contained in [9] and [10]. [ABSTRACT FROM AUTHOR]

In this paper, we prove some results about that what happens if we take trace of symmetric bi-derivation or permuting tri-derivation instead of derivation in definition of generalized derivation. Also we apply these results to very well-known results. [ABSTRACT FROM AUTHOR]

We define and study the extended centroid of a prime semiring. We show that the extended centroid is a semifield and give some properties of the centroid of a right multiplicatively cancellable prime semiring. [ABSTRACT FROM AUTHOR]

The aims of this paper are introduce the notions of symmetric bi-derivation and generalized derivation in MV-algebras and investigate some of their properties. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a permuting tri-(σ,τ ) -derivation and permuting tri-generalized derivation in a near ring and generalize some of the results in [4], [6], [8]. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate certain results on 3-prime near-rings and generalize these results on near-rings to semi-group ideals of 3-prime near-rings. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of permuting tri-derivations in lattices and to study some properties of permuting tri-derivations. [ABSTRACT FROM AUTHOR]

In [7] ,Öztürk has proved some results concerning permuting tri-derivations on prime and semi-prime rings. We study permuting tri-additive maps with trace which is skew-commuting or skew-centralizing on s-unital rings and also we obtain a few results on trace of permuting tri-derivations in prime rings. [ABSTRACT FROM AUTHOR]