Reduction of Quasi-Lattices to Lattices

C. Ganesa Moorthy; SG. Karpagavalli

doi:https://doi.org/10.14445/22315373/IJMTT-V65I4P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 4 | Year 2019 | Article Id. IJMTT-V65I4P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I4P506

Reduction of Quasi-Lattices to Lattices

C. Ganesa Moorthy, SG. Karpagavalli

Abstract

Quasi-lattices are introduced in terms of `join' and `meet' opera- tions. It is observed that quasi-lattices become lattices when these op- erations are associative and when these operations satisfy `modularity' conditions. A fundamental theorem of homomorphism proved in this article states that a quasi-lattice can be mapped onto a lattice when some conditions are satisfied.

Keywords

Minimal upper bound, Congruence relation, Partition.

References

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[4] E.T.Schmidt, Semimodular lattices and the Hall-Dilworth gluing con-struction, Acta.Math.Hungar, 127(3)(2010) 220-224.
[5] P.Terraf, Factor congruences in semilattices, Revista de la Union Mathematica Argentina, 52(2011) 1-10.
[6] F.Wehrung , A solution to Dilworth's congruence lattice problem, Advances in Mathematics, 216(2007) 610-625.

Citation :

C. Ganesa Moorthy, SG. Karpagavalli, "Reduction of Quasi-Lattices to Lattices," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 4, pp. 28-35, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I4P506