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Full-Text Articles in Physical Sciences and Mathematics
On Hypersemigroups, Niovi Kehayopulu
On Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
This is from the paper "Hypergroupes canoniques values et hypervalues" by J. Mittas in Mathematica Balkanica 1971: "The concept of hypergroup introduced by Fr. MARTY in 1934 [Actes du Congres des Math. Scand. Stocholm 1935, p. 45] is as follows: "A hypergroup is a nonempty set $H$ endowed with a multiplication $xy$ such that, for every $x,y,z\in H,$ the following hold: (1) $xy\subseteq H$; (2) $x(yz)=(xy)z$ and (3) $xH=Hx=H$. The first condition expresses that the multiplication is an hyperoperation on $H$, in other words, the composition of two elements $x,y$ of $H$ is a subset of $H$. It is very …
Finite Ordered $\Gamma$-Hypersemigroups Constructed By Ordered $\Gamma$-Semigroups, Niovi Kehayopulu
Finite Ordered $\Gamma$-Hypersemigroups Constructed By Ordered $\Gamma$-Semigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
In the investigation of ordered $\Gamma$-hypersemigroups we often need counterexamples (of finite order) given by a table of multiplication and a figure that are impossible to make by hand and very difficult to write programs as well. So it is useful to have examples of ordered $\Gamma$-semigroups for which is much more easier to write programs and then from these examples to obtain corresponding examples of ordered $\Gamma$-hypersemigroups. In this respect we show that from every example of a regular, intra-regular, right (left) regular, right (left) quasi-regular, semisimple, right (left) simple, simple, strongly regular ordered $\Gamma$-semigroup given by a table …
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 …
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.
Regularity Of Semigroups Of Transformations With Restricted Range Preserving An Alternating Orientation Order, Somphong Jitman, Rattana Srithus, Chalermpong Worawannotai
Regularity Of Semigroups Of Transformations With Restricted Range Preserving An Alternating Orientation Order, Somphong Jitman, Rattana Srithus, Chalermpong Worawannotai
Turkish Journal of Mathematics
It is well known that the transformation semigroup on a nonempty set $X$, which is denoted by $T(X)$, is regular, but its subsemigroups do not need to be. Consider a finite ordered set $X=(X;\leq)$ whose order forms a path with alternating orientation. For a nonempty subset $Y$ of $X$, two subsemigroups of $T(X)$ are studied. Namely, the semigroup $OT(X,Y)=\{\alpha\in T(X)\mid \alpha~\text{is order-preserving and }X\alpha\subseteq Y\}$ and the semigroup $OS(X,Y)=\{\alpha\in T(X)\mid\alpha$ is order-preserving and $Y\alpha \subseteq Y\}$. In this paper, we characterize ordered sets having a coregular semigroup $OT(X,Y)$ and a coregular semigroup $OS(X,Y)$, respectively. Some characterizations of regular semigroups $OT(X,Y)$ …