On hypersemigroups

TL;DR

This paper introduces hypersemigroups, explaining their relation to semigroups and emphasizing the importance of sets over points in their structure, serving as an educational example.

Contribution

It provides a foundational explanation of hypersemigroups, illustrating their connection to semigroups and clarifying their structural properties.

Findings

Hypersemigroups extend semigroup concepts.

Points are non-essential in hypersemigroup ideals.

Sets are fundamental in hypersemigroup structure.

Abstract

In this paper we show the way we pass from semigroups (without order) to hypersemigroups. Moreover we show that, exactly as in semigroups, in the results of hypersemigroups based on right (left) ideals, quasi-ideals and bi-ideals, points do not play any essential role, but the sets, which shows their pointless character. The aim of writing this paper is not just to add a publication on hypersemigroups but, mainly, to publish a paper which serves as an example to show what an hypersemigroup is and give the right information concerning this structure.