Vector Valued Hyperstructures

V. Miovska, V. Celakoska-Jordanova, B. Davvaz

Vector valued hyperstructures, i.e., $(n,m)$-hyperstructures, where $n=m+k$, $k\geq 1$, 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.