From rings to minimal Hv-fields

Document Type : Original Article


Emeritus Professor of Mathematics, Democritus University of Thrace, Greece


The class of Hv-structures is the largest class of hyperstructures defined on the same set. For this reason, they have applications in mathematics and in other sciences, which range from biology, hadronic physics, leptons, linguistics, sociology, to mention but a few. They satisfy the weak axioms where the non-empty intersection replaces equality. The fundamental relations connect, by quotients, the Hv-structures with the classical ones. In order to specify the appropriate hyperstructure as a model for an application which fulfill 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-field, and they are used in representation theory. In this presentation we focus on minimal Hv-fields derived from rings.