Turkish Journal of Mathematics
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 $S$.
DOI
10.3906/mat-2011-35
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, N (2021). On ordered $\Gamma$-hypersemigroups, minimal bi-ideals, and minimal left ideals. Turkish Journal of Mathematics 45 (2): 909-918. https://doi.org/10.3906/mat-2011-35
