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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. [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]

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]