On strong-inverse elements

Hyperstructures have applications in mathematics and in other sciences. For this, the largest class of the hyper- structures, the Hv-structures, is used. 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. Since the number of Hv-structures dened on the same set is very big, it is important to study special elements. A lot of those special elements are not appeared in the classical theory therefore, one has to discover their properties from the beginning. We continuous our study on Hv-structures which have the so called strong inverse elements.