Distributive lattices with strong endomorphism kernel property as direct sums

Document Type: Research Paper

Author

Department of Algebra and Geometry, Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava, Slovakia.

Abstract

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.

Keywords


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