%0 Journal Article
%T Distributive lattices with strong endomorphism kernel property as direct sums
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Gurican, Jaroslav
%D 2020
%\ 07/01/2020
%V 13
%N 1
%P 45-54
%! Distributive lattices with strong endomorphism kernel property as direct sums
%K unbounded distributive lattice
%K strong endomorphism kernel property
%K congruence relation
%K bounded Priestley space
%K Priestley duality
%K strong element
%K direct sum
%R 10.29252/cgasa.13.1.45
%X Unbounded distributive lattices which have strong endomorphism kernel property (SEKP) introduced by Blyth and Silva in [3] were fully characterized in [11] using Priestley duality (see TheoremÂ 2.8}). We shall determine the structure of special elements (which are introduced afterÂ Theorem 2.8 under the name strong elements) and show that these lattices can be considered as a direct product of three lattices, a lattice with exactly one strong element, a lattice which is a direct sum of 2 element lattices with distinguished elements 1 and a lattice which is a direct sum of 2 element lattices with distinguished elements 0, and the sublattice of strong elements is isomorphic to a product of last two mentioned lattices.
%U https://cgasa.sbu.ac.ir/article_87512_30a0285f83407ee46e5bc8449eb777a0.pdf