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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 …
On $\Gamma$-Hypersemigroups, Niovi Kehayopulu
On $\Gamma$-Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
The results on $\Gamma$-hypersemigroups are obtained either as corollaries of corresponding results on $\vee e$ or $poe$-semigroups or on the line of the corresponding results on $le$-semigroups. It has come to our attention that Theorem 3.22 in [4] cannot be obtained as corollary to Theorem 2.2 of the same paper as for a $\Gamma$-hypersemigroup, $({\cal P}^*(M),\Gamma,\subseteq)$ is a $\vee e$-semigroup and not an $le$-semigroup. Also on p. 1850, l. 12 in [4], the "$le$-semigroup" should be changed to "$\vee e$-semigroup". In the present paper we prove Theorems 3.26 and 3.28 stated without proof in [4]. On this occasion, some further …
Lattice Ordered Semigroups And $\Gamma$-Hypersemigroups, Niovi Kehayopulu
Lattice Ordered Semigroups And $\Gamma$-Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
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.
From Ordered Semigroups To Ordered Hypersemigroups, Niovi Kehayopulu
From Ordered Semigroups To Ordered Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
In an attempt to show the way we pass from ordered semigroups to ordered hypersemigroups, we examine some well known results of regular and intraregular ordered semigroups in case of ordered hypersemigroups. The corresponding results on hypersemigroups (without order) can also be obtained as application of the results of the present paper. The sets we use in our investigation shows the pointless character of the results.
Lattice Ordered Semigroups And Hypersemigroups, Niovi Kehayopulu
Lattice Ordered Semigroups And Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
This paper shows that many results on hypersemigroups do not need any proof as can be obtained from lattice ordered semigroups.
On Ordered Hypersemigroups Given By A Table Of Multiplication And A Figure, Niovi Kehayopulu
On Ordered Hypersemigroups Given By A Table Of Multiplication And A Figure, Niovi Kehayopulu
Turkish Journal of Mathematics
The aim is to show that from every example of a regular, intraregular, left (right) regular, left (right) quasiregular, semisimple, left (right) simple, simple, or strongly simple ordered semigroup given by a table of multiplication and an order, a corresponding example of regular, intraregular, left (right) regular, left (right) quasiregular, semisimple, left (right) simple, simple, or strongly simple ordered hypersemigroup can be constructed having the same left (right) ideals, bi-ideals, quasi-ideals, or interior ideals. On this occasion, some further related results have also been given.