Lattice ordered semigroups and hypersemigroups
Lattice ordered semigroups and hypersemigroups
This paper shows that many results on hypersemigroups do not need any proof as can be obtained fromlattice ordered semigroups.
___
- [1] Birkhoff G. Lattice Theory. Revised Ed. American Mathematical Society Colloquium Publications Vol. XXV.
Providence, RI, USA: American Mathematical Society, 1961.
- [2] Birkhoff G. Lattice Theory. Corrected Reprint of the 1967 Third Edition. American Mathematical Society Colloquium
Publications Vol. XXV. Providence, RI, USA: American Mathematical Society, 1979.
- [3] Clifford AH, Preston GB. The Algebraic Theory of Semigroups. Vol. I. Mathematical Surveys, No. 7 Providence,
RI, USA: American Mathematical Society, 1961.
- [4] Corsini P. Hypergroupes et groupes ordonnes. Rendiconti del Seminario Matematico della Università di Padova
1972; 48: 189-204 (in French with Italian and English summaries).
- [5] Dubreil-Jacotin ML, Lesieur L, Croisot R. Leçons sur la Théorie des Treillis des Structures Algébriques Ordonnées
et des Treillis Géométriques. Paris, France: Gauthier-Villars, 1953 (in French).
- [6] Fuchs L. Partially Ordered Algebraic Systems. Oxford, UK: Wesley Publishing, 1963.
- [7] Kehayopulu N. A characterization of some regular duo le-semigroups. Contributions to general algebra. In: Proceedings
of Klagenfurt Conference; Klagenfurt, Austria; Verlag Johannes Heyn, 1979. pp. 137-143.
- [8] Kehayopulu N. On intra-regular ∨e-semigroups. Semigroup Forum 1980; 19: 111-121.
- [9] Kehayopulu N. A characterization of regular le-semigroups. Semigroup Forum 1981; 23: 85-86.
- [10] Kehayopulu N. On regular le-semigroups. Semigroup Forum 1984; 28: 371-372.
- [11] Kehayopulu N. On semilattices of simple poe-semigroups. Mathematica Japonica 1993; 38: 305-318.
- [12] Kehayopulu N. On hypersemigroups. Pure Mathematics and Applications 2015; 25: 151-156.
- [13] Kehayopulu N. On le-semigroups. Turkish Journal of Mathematics 2016; 40: 310-316.
- [14] Kehayopulu N. Hypersemigroups and fuzzy hypersemigroups. European Journal of Pure and Applied Mathematics
2017; 10: 929-945.
- [15] Kehayopulu N. How we pass from semigroups to hypersemigroups. Lobachevskii Journal of Mathematics 2018; 39:
121-128.
- [16] Kehayopulu N. On ordered hypersemigroups with idempotent ideals, prime or weakly prime ideals. European Journal
of Pure and Applied Mathematics 2018; 11: 10-22.
- [17] Marty F. Sur une généralization de la notion de groupe. Actes du Congrès des Mathematica Scandinavica Stockholf
1934.
- [18] Mittas J. Sur une classe d’hypergroupes commutatifs. Comptes Rendus Mathematique Academie des Sciences Paris
1969; Series A-B 269: A485-A488 (in French).
- [19] Mittas J. Hypergroupes canoniques valués et hypervalués. Mathematica Balkanica 1971; 1: 181-185.