From rings to minimal Hv-fields

The class of Hv-structures is the largest class of hyper- structures dened on the same set. For this reason, they have applications in mathematics and in other sciences, which range from biology, hadronic physics, leptons, lin- guistics, sociology, to mention but a few. They satisfy the weak axioms where the non-empty intersection replaces equality. The fundamental relations connect, by quo- tients, the Hv-structures with the classical ones. In or- der to specify the appropriate hyperstructure as a model for an application which fulll a number of properties, the researcher can start from the basic ones. Thus, the researcher must know the minimal hyperstructures. Hv- numbers are elements of Hv-eld, and they are used in representation theory. In this presentation we focus on minimal Hv-elds derived from rings.