Geodesic
From ∨e-Semigroups to Hypersemigroups
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 113-126.

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A poe-semigroup is a semigroup S at the same time an ordered set having a greatest element “e” in which the multiplication is compatible with the ordering. A ∨e-semigroup is a semigroup S at the same time an upper semilattice with a greatest element “e” such that a(b ∨ c) = ab ∨ ac and (a ∨ b)c = ac ∨ bc for every a, b, c ∈ S. If S is not only an upper semi-lattice but a lattice, then it is called le-semigroup. From many results on le-semigroups, ∨e-semigroups or poe-semigroups, corresponding results on ordered semigroups (without greatest element) can be obtained. Related results on hypersemigroups or ordered hypersemigroups follow as application. An example is presented in the present note; the same can be said for every result on these structures. So order-lattices play an essential role in studying the hypersemigroups and the ordered hypersemigroups.
Keywords: ∨ e -semigroup, hypersemigroup, ( m, n )-ideal (element), regular, left regular, completely regular 
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Kehayopulu, Niovi. From ∨e-Semigroups to Hypersemigroups. Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 113-126. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_1_a9/

[1] G. Birkhoff, Lattice Theory, Revised ed. American Mathematical Society Colloquium Publications, Vol. XXV American Mathematical Society (Providence R.I., 1961) xiii+283 pp.

[2] M.L. Dubreil-Jacotin, L. Lesieur and R. Croisot, Leçons sur la Théorie des Treillis des Structures Algébriques Ordonnées et des Treillis Géométriques (Gauthier-Villars, Paris, 1953) viii+385 pp.

[3] L. Fuchs, Partially Ordered Algebraic Systems, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto (Calif.-London, 1963) ix+229 pp.

[4] N. Kehayopulu, On intra-regular ∨ e-semigroups, Semigroup Forum 19 (1980) 111–121. doi:10.1007/BF02676636

[5] N. Kehayopulu, Generalized ideal elements in poe-semigroups, Semigroup Forum 25 (1982) 213–222. doi:10.1007/BF02573600

[6] N. Kehayopulu, On weakly prime ideals of ordered semigroups, Math. Japon. 35 (1990) 1051–1056.

[7] N. Kehayopulu, On right regular and right duo ordered semigroups, Math. Japon. 36 (1991) 201–206.

[8] N. Kehayopulu, On completely regular poe-semigroups, Math. Japon. 37 (1992) 123–130.

[9] N. Kehayopulu, On regular duo ordered semigroups, Math. Japon. 37 (1992) 535–540.

[10] N. Kehayopulu, On regular, intra-regular ordered semigroups, Pure Math. Appl. 4 (1993) 447–461.

[11] N. Kehayopulu, On regular, regular duo ordered semigroups, Pure Math. Appl. 5 (1994) 161–176.

[12] N. Kehayopulu, On hypersemigroups, Pure Math. Appl. (PU.M.A.) 25 (2015) 151–156. doi:10.1515/puma-2015-0015

[13] N.Kehayopulu, Hypersemigroups and fuzzy hypersemigroups, Eur. J. Pure Appl. Math. 10 (2017) 929–945.

[14] N. Kehayopulu, Left regular and intra-regular ordered hypersemigroups in terms of semiprime and fuzzy semiprime subsets, Sci. Math. Jpn. 80 (2017) 295–305.

[15] N. Kehayopulu, How we pass from semigroups to hypersemigroups, Lobachevskii J. Math. 39 (2018) 121–128. doi:10.1134/S199508021801016X

[16] N. Kehayopulu, On ordered hypersemigroups with idempotent ideals, prime or weakly prime ideals, Eur. J. Pure Appl. Math. 11 (2018) 10–22. doi:10.29020/nybg.ejpam.v11i1.3085

[17] N. Kehayopulu, From ordered semigroups to ordered hypersemigroups, Turkish J. Math. 43 (2019) 21–35. doi:10.3906/mat-1806-104

[18] N. Kehayopulu, Lattice ordered semigroups and hypersemigroups, Turkish J. Math. 43 (2019) 2592–2601. doi:10.3906/mat-1907-86