Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585313120200701Distributive lattices with strong endomorphism kernel property as direct sums45548751210.29252/cgasa.13.1.45ENJaroslav GuricanDepartment of Algebra and Geometry,
Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava, Slovakia.0000-0002-2857-161XJournal Article20200607Unbounded 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.https://cgasa.sbu.ac.ir/article_87512_30a0285f83407ee46e5bc8449eb777a0.pdf