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Full-Text Articles in Physical Sciences and Mathematics
On Ordered $\Gamma$-Hypersemigroups, Minimal Bi-Ideals, And Minimal Left Ideals, Niovi Kehayopulu
On Ordered $\Gamma$-Hypersemigroups, Minimal Bi-Ideals, And Minimal Left Ideals, Niovi Kehayopulu
Turkish Journal of Mathematics
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 $S$.
On Ordered $\Gamma$-Hypersemigroups And Their Relation To Lattice Ordered Semigroups, Niovi Kehayopulu
On Ordered $\Gamma$-Hypersemigroups And Their Relation To Lattice Ordered Semigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
The concept of $\Gamma$-hypersemigroup has been introduced in Turk J Math 2020; 44 (5): 1835-1851 in which it has in which it has been shown that various results on $\Gamma$-hypersemigroups can be obtained directly as corollaries of more general results from the theory of $le$-semigroups (i.e. lattice ordered semigroups having a greatest element) or $poe$-semigroups. As a continuation of the paper mentioned above, in the present paper, the concept of ordered $\Gamma$-hypersemigroups has been introduced, and their relation to lattice ordered semigroups is given. It has been shown that although the results on ordered $\Gamma$-hypersemigroups cannot be obtained as corollaries …