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Full-Text Articles in Physical Sciences and Mathematics
Adjunction Greatest Element To Ordered Hypersemigroups, Niovi Kehayopulu
Adjunction Greatest Element To Ordered Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
As a continuation of the paper "Adjunction Identity to Hypersemigroup" in Turk J Math 2022; 46 (7): 2834--2853, it has been proved here that the adjunction of a greatest element to an ordered hypersemigroup is actually an embedding problem. The concept of pseudoideal has been introduced and has been proved that for each ordered hypersemigroup $S$ an ordered hypersemigroup $V$ having a greatest element ($poe$-hypersemigroup) can be constructed in such a way that there exists a pseudoideal $T$ of $S$ such that $S$ is isomorphic to $T$. If $S$ does not have a greatest element, then this can be regarded …
What Can Lattices Do For Hypersemigroups?, Niovi Kehayopulu
What Can Lattices Do For Hypersemigroups?, Niovi Kehayopulu
Turkish Journal of Mathematics
This is from Birkhoff, the "father of lattice theory" in Trends in Lattice Theory. Van Nostrand 1970: "Lattices can do things for you, no matter what kind of mathematician you are!". The aim of this paper is to show that the $le$-semigroups (lattice ordered semigroups possessing a greatest element) play the main role in studying the ordered hypersemigroups. From many results on lattice ordered semigroups corresponding results on ordered semigroups can be obtained. The converse is also possible but the beauty and simplicity of "order" makes it easier to investigate the lattice ordered semigroup at first. After getting the results …