A Class of Congruencies on Distributive Semilattice (Revista de Investigaciones Universidad del Quindío, 2022)
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.
Keywords: Congruence class of semilattice; Distributive Semilattice; Natural epimorphism of semilattice; Quotient semilattice