Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1909-83
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
First Page
1835
Last Page
1851
Recommended Citation
KEHAYOPULU, NIOVI
(2020)
"Lattice ordered semigroups and $\Gamma$-hypersemigroups,"
Turkish Journal of Mathematics: Vol. 44:
No.
5, Article 25.
https://doi.org/10.3906/mat-1909-83
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss5/25
