TY - JOUR
ID - 87512
TI - Distributive lattices with strong endomorphism kernel property as direct sums
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Gurican, Jaroslav
AD - Department of Algebra and Geometry,
Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava, Slovakia.
Y1 - 2020
PY - 2020
VL - 13
IS - 1
SP - 45
EP - 54
KW - unbounded distributive lattice
KW - strong endomorphism kernel property
KW - congruence relation
KW - bounded Priestley space
KW - Priestley duality
KW - strong element
KW - direct sum
DO - 10.29252/cgasa.13.1.45
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_87512.html
L1 - https://cgasa.sbu.ac.ir/article_87512_30a0285f83407ee46e5bc8449eb777a0.pdf
ER -