TY  - JOUR
N2  - 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.
IS  - 3-4
N1  - Bibliogr.: p. 412-413. ; ill. ; összefoglalás angol nyelven
Y1  - 2021///
SN  - 2064-8316
CY  - Szeged
SP  - 381
KW  - Matematika
KW  -  Algebra
A1  -  Czédli Gábor
ID  - acta75847
JF  - Acta scientiarum mathematicarum
UR  - http://acta.bibl.u-szeged.hu/75847/
VL  - 87
TI  - Lamps in slim rectangular planar semimodular lattices
EP  - 413
AV  - restricted
ER  -