Hyperstructure
Hyperstructures are algebraic structures equipped with at least one multi-valued operation, called a hyperoperation. The largest classes of the hyperstructures are the ones called – structures.
A hyperoperation on a nonempty set is a mapping from to the nonempty power set, meaning the set of all nonempty subsets of, i.e.
If then we define
is a semihypergroup if is an associative hyperoperation, i.e.
Furthermore, a hypergroup is a semihypergroup, where the reproduction axiom is valid, i.e.
