Congruence Lattices of Uniform Lattices

I.Athal; M.Karthivel

doi:https://doi.org/10.14445/22315373/IJMTT-V44P514

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 44 | Number 2 | Year 2017 | Article Id. IJMTT-V44P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P514

Congruence Lattices of Uniform Lattices

I.Athal, M.Karthivel

Abstract

In this chapter we prove that every finite distributive lattice D can be represented as the congruence lattice of finite uniform lattice L. Infact we prove that “For any finite distributive lattice D, there exists a finite uniform lattice L such that the congruence lattice of L is isomorphic to D, and L satisfies the properties (P) and (Q) where (P) Every join-irreducible congruence of L we introduce a very simple kind of chopped lattices.

Keywords

we prove that the ideal lattice of this chopped lattice is uniform.

References

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Citation :

I.Athal, M.Karthivel, "Congruence Lattices of Uniform Lattices," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 2, pp. 71-75, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P514