Relations on Krasner (m,n)(m,n)-hyperrings

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