Minimal representations of a finite distributive lattice by principal congruences of a lattice

Grätzer, George A. and Lakser, Harry: Minimal representations of a finite distributive lattice by principal congruences of a lattice. Acta scientiarum mathematicarum, (85) 1-2. pp. 69-96. (2019)

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Abstract

Let the finite distributive lattice D be isomorphic to the congruence lattice of a finite lattice L. Let Q denote those elements of D that correspond to principal congruences under this isomorphism. Then Q contains 0, 1 ∈ D and all the join-irreducible elements of D. If Q contains exactly these elements, we say that L is a minimal representation of D by principal congruences of the lattice L. We characterize finite distributive lattices D with a minimal representation by principal congruences with the property that D has at most two dual atoms.

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2019
Volume: 85
Number: 1-2
Page Range: pp. 69-96
ISSN: 2064-8316
DOI: https://doi.org/10.14232/actasm-017-060-9
Uncontrolled Keywords: Matematika
Additional Information: Bibliogr.: p. 95-96. ; összefoglalás angol nyelven
Official URL: http://www.acta.hu
Date Deposited: 2019. Sep. 25. 10:01
Last Modified: 2019. Sep. 25. 10:01
URI: http://acta.bibl.u-szeged.hu/id/eprint/62134

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