%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 Theorem  2.8}). We shall determine the structure of special elements (which are introduced after  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