Relations on Krasner [formula omitted]-hyperrings

Abstract

The aim of this research work is to define and characterize a new class of n -ary multialgebras that we call Krasner ( m , n ) -hyperrings. They are a generalization of canonical n -ary hypergroups, a generalization of ( m , n ) -rings, a generalization of hyperrings in the sense of Krasner and a subclass of the ( m , n ) -hyperrings. Also, the three isomorphism theorems of ring theory and Krasner hyperring theory are derived in the context of Krasner ( m , n ) -hyperrings.