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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]