Lamps in slim rectangular planar semimodular lattices

Czédli Gábor: Lamps in slim rectangular planar semimodular lattices. In: Acta scientiarum mathematicarum, (87) 3-4. pp. 381-413. (2021)

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Abstract

A planar (upper) semimodular lattice L is slim if the five-element nondistributive modular lattice M3 does not occur among its sublattices. (Planar lattices are finite by definition.) Slim rectangular lattices as particular slim planar semimodular lattices were defined by G. Grätzer and E. Knapp in 2007. In 2009, they also proved that the congruence lattices of slim planar semimodular lattices with at least three elements are the same as those of slim rectangular lattices. In order to provide an effective tool for studying these congruence lattices, we introduce the concept of lamps of slim rectangular lattices and prove several of their properties. Lamps and several tools based on them allow us to prove in a new and easy way that the congruence lattices of slim planar semimodular lattices satisfy the two previously known properties. Also, we use lamps to prove that these congruence lattices satisfy four new properties including the Two-pendant Four-crown Property and the Forbidden Marriage Property.

Item Type:	Article
Heading title:	Algebra
Journal or Publication Title:	Acta scientiarum mathematicarum
Date:	2021
Volume:	87
Number:	3-4
ISSN:	2064-8316
Page Range:	pp. 381-413
Language:	English
Place of Publication:	Szeged
Related URLs:	http://acta.bibl.u-szeged.hu/75796/
DOI:	10.14232/actasm-021-865-y
Uncontrolled Keywords:	Matematika, Algebra
Additional Information:	Bibliogr.: p. 412-413. ; ill. ; összefoglalás angol nyelven
Subjects:	01. Natural sciences 01. Natural sciences > 01.01. Mathematics
Date Deposited:	2022. May. 24. 11:45
Last Modified:	2022. May. 24. 12:58
URI:	http://acta.bibl.u-szeged.hu/id/eprint/75847

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