Turkish Journal of Mathematics
It has been shown in Turk J Math 2019; 43 (5): 2592-2601 that many results on hypersemigroups can be obtained directly as corollaries of more general results from the theory of lattice ordered semigroups, $\vee e$-semigroups or $poe$-semigroups. The present note shows that although this is not exactly the case for ordered hypersemigroups, even in this case various results may be suggested from analogous results for $le$, $\vee e$ or $poe$-semigroups and direct proofs derive along the lines of those $le$, $\vee e$ or $poe$-semigroups setting as well; the sets in the investigation provides a further indication that the results on this structure come from the lattice ordered semigroups or ordered semigroups in general. In many cases, whenever we have a look at any result on lattice ordered semigroups, we immediately know if can be transferred to ordered hypersemigroups. We never work on ordered hypersemigroups directly.
$le$-semigroup, hypersemigroup, ideal element, ideal, meet-irreducible, semisimple
"Relationship between lattice ordered semigroups and ordered hypersemigroups,"
Turkish Journal of Mathematics: Vol. 45:
4, Article 19.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss4/19