Revista de Investigaciones Universidad del Quindío (Dec 2022)

A Class of Congruencies on Distributive Semilattice

  • Tolesa Dekeba Bekele,
  • Tesfu Reta

DOI
https://doi.org/10.33975/riuq.vol34n1.525
Journal volume & issue
Vol. 34, no. 1

Abstract

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In this paper we, contribute the notation of natural epimorphism of a semilattice on the quotient semilattice and subsemilattice. If S is distributive semilattice and F is a filter of S, then we demonstrate that θF is the smallest congruence on S containing F in a single equivalence class and that S/θF is distributive. In addition, the author proved that map FθF is an isomorphism from the lattice of F0(S) all non-empty filters of S into a permutable sublattice of the lattice C(S) of all congruencies on S.

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