Extended centroid of hyperrings

Abstract

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.