The Maximal Hyperrings of Quotients

Abstract

We show that the maximal quotient hyperring Q(mr)(R) of a semiprime hyperring R can be obtained in a similar way to a maximal quotient ring. In this regard we introduce and study some basic notions of hyperrings such as dense hyperideal, essential hyperideal, singular hyperideal and prove some results satisfying them. Finally, we show that if R is a semiprime hyperring and Q = Q(mr)(R), then Q is regular (in the sense of von Neumann) if and only if R has a zero right singular hyperideal.