On Regular Hypersemigroups

Niovi Kehayopulu

Abstract

It is shown that an hypersemigroup (S, ◦) is regular if and only if the set of all quasi-ideals of S with the operation “∗” is a von Neumann regular semigroup. It is both regular and intra-regular if and only if the set of all quasi-ideals of S with the operation “∗” is a band.

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