H_v-structures associated with PQ-hyperoperations

Abstract

The object of this article is the H_v -modules. These are generalizations of the known hypermodules 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 H_v -modules is the class of H_v -modules with external P-hyperoperations or P-H_v -modules. In this article, we introduce PQ-hyperoperations which generalize P-hyperoperations. In this respect, some theorems about PQ-hyperoperations are proved. Also, the homomorphisms between PQ-Hv-modules are studied.

Finally, we study homomorphisms on PQ-H_v -modules and show that every exact sequence of R-modules induces an exact sequence of PQ-H_v -modules in the sense of [3].

Keywords:

• H_v-modules
• P-hyperoperation
• exact sequence