H_v-Fields, h/v-Fields

Abstract

Last decades the hyperstructures have a lot of applications in mathematics and in other sciences. These applications range from biomathematics and hadronic physics to linguistic and sociology. For applications the largest class of the hyperstructures, the H v -structures, is used, they satisfy the weak axioms where the non-empty intersection replaces the equality. The main tools in the theory of hyperstructures are the fundamental relations which connect, by quotients, the H v -structures with the corresponding classical ones. These relations are used to define hyperstructures as H v -fields, H_v-vector spaces and so on, as well. The extension of the reproduction axiom, from elements to fundamental classes, introduces the extension of H_v-structures to the class of h/v-structures. We focus our study mainly in the relation of these classes and we present some constructions on them.

Keywords

• hope
• H v -structure
• h/v-structure
• H v -field
• h/v-field