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.

10.29252/cgasa.13.1.45

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.

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References

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Categories and General Algebraic Structures with Applications
Volume 13, Issue 1
July 2020
Pages 45-54

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