Isomorphism Theorems on PQ-hyperstructures
The object of this paper is the Hv-ring. These are generalizations of the known hyperrings where axioms are replaced by the weak ones, that is, instead of the equality on sets, one has non-empty intersections. A wide class of Hv-rings is the class of the P-Hv-rings. The main purpose of this article is to introduce a new sort of hyperoperation on a Hv-ring, called PQ hyperoperation which is a generalization of P-hyperoperation introduced by T. Vougiouklis in 1987. In this respect, some isomorphism theorems about PQ–Hv-rings are presented and some interesting properties of the fundamental relation, i.e, the smallest equivalence relation for which the quotient is a ring, are investigated.
Keywords: Hv-ring, P-hyperoperation.
AMS subject classification: 20N20