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
on a nonempty set
to the nonempty power set
, meaning the set of all nonempty subsets of
is an associative hyperoperation, i.e.
Furthermore, a hypergroup is a semihypergroup
, where the reproduction axiom is valid, i.e.
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