Turkish Journal of Mathematics
DOI
10.3906/mat-2011-35
Abstract
The definition of ordered $\Gamma$-hypersemigroups and the definitions of regular and intra-regular ordered $\Gamma$-hypersemigroups in the existing bibliography should be corrected. Care should be given to the definitions of bi-$\Gamma$-hyperideals and quasi-$\Gamma$-hyperideals as well. The main results are a characterization of minimal bi-ideals of an ordered $\Gamma$-hypersemigroup $S$ in terms of $\cal B$-simple bi-ideals of $S$ and a characterization of minimal left (resp. right) ideals of an ordered $\Gamma$-hypersemigroup $S$ in terms of left (resp. right) simple subsemigroups of $S$.
Keywords
Ordered $\Gamma$-hypersemigroup, regular, intra-regular, bi-$\Gamma$-hyperideal, quasi-$\Gamma$-hyperideal, ${\cal B}$-simple bi-idea
First Page
909
Last Page
918
Recommended Citation
KEHAYOPULU, NIOVI
(2021)
"On ordered $\Gamma$-hypersemigroups, minimal bi-ideals, and minimal left ideals,"
Turkish Journal of Mathematics: Vol. 45:
No.
2, Article 19.
https://doi.org/10.3906/mat-2011-35
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss2/19
