Lattice ordered semigroups and $\Gamma$-hypersemigroups

Authors: NIOVI KEHAYOPULU

Abstract: As we have already seen in Turkish Journal of Mathematics (2019) 43: 2592-2601 many results on hypersemigroups do not need any proof as they can be obtained from lattice ordered semigroups. The present paper goes a step further, to show that many results on $\Gamma$-hypersemigroups as well can be obtained from lattice ordered semigroups. It can be instructive to prove them directly, but even in that case the proofs go along the lines of lattice ordered semigroups (or $poe$-semigroups). In the investigation, we faced the problem to correct the definition of $\Gamma$-hypersemigroups given in the existing bibliography.

Keywords: Lattice ordered semigroup, $\Gamma$-hypersemigroup, regular, intra-regular, right (left) ideal element, right (left) ideal, bi-ideal element, bi-ideal, right (left) regular, right (left) simple

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