Vector valued hyperstructures

Abstract

Vector valued hyperstructures, i.e., (n,m)-hyperstructures, where n = m + k, k >= 1, as a generalization of vector valued structures and n-ary hyperstructures are introduced and supported by many examples. We have presented some initial properties about (n,m)-hypersemigroups and (n,m)-hypergroups. Moreover, by properly defining regular and strongly regular binary relations, from vector valued hypersemigroups (hypergroups) we obtain "ordinary" vector valued semigroups (groups) on quotients.