@article {
author = {Gurican, Jaroslav},
title = {Distributive lattices with strong endomorphism kernel property as direct sums},
journal = {Categories and General Algebraic Structures with Applications},
volume = {13},
number = {1},
pages = {45-54},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {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 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.},
keywords = {unbounded distributive lattice,strong endomorphism kernel property,congruence relation,bounded Priestley space,Priestley duality,strong element,direct sum},
url = {https://cgasa.sbu.ac.ir/article_87512.html},
eprint = {https://cgasa.sbu.ac.ir/article_87512_30a0285f83407ee46e5bc8449eb777a0.pdf}
}