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Abelizations of weakly associative hyperstructures based on their direct squares. (English) Zbl 1110.20304

Summary: The paper contains a simple construction of some types of commutative hyperstructures as hypergroupoids, weakly associative semi-hypergroupoids, hypergroups, quasi-hypergroups and weakly associative hyperrings from non-commutative hyperstructures. It is proved that the used construction induces reflectors on suitable categories of the mentioned hyperstructures.

MSC:

20N20 Hypergroups
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
16Y99 Generalizations
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