Notes on planar semimodular lattices. VIII. Congruence lattices of SPS lattices

被引：8
|
作者：
Gratzer, G. [1 ]
机构：
[1] Univ Manitoba, Dept Math, Winnipeg, MB, Canada
来源：
ALGEBRA UNIVERSALIS | 2020年 / 81卷 / 02期
关键词：
Lattice; Congruence; Semimodular; Planar; Slim; SLIM;
D O I：
10.1007/s00012-020-0641-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note, I find a new property of the congruence lattice, Con L, of an SPS lattice L (slim, planar, semimodular, where "slim" is the absence of M-3 sublattices) with more than 2 elements: there are at least two dual atoms in ConL. So the three-element chain cannot be represented as the congruence lattice of an SPS lattice, supplementing a result of G. Czedli.
引用
收藏
页数：3
相关论文
共 50 条
  • [31] Infinitely many new properties of the congruence lattices of slim semimodular lattices
    Gábor Czédli
    Acta Scientiarum Mathematicarum, 2023, 89 : 319 - 337
  • [32] D Congruence structure of planar semimodular lattices: the General Swing Lemma
    Czedli, Gabor
    Gratzer, George
    Lakser, Harry
    ALGEBRA UNIVERSALIS, 2018, 79 (02)
  • [33] An extension theorem for planar semimodular lattices
    Graetzer, G.
    Schmidt, E. T.
    PERIODICA MATHEMATICA HUNGARICA, 2014, 69 (01) : 32 - 40
  • [34] An extension theorem for planar semimodular lattices
    G. Grätzer
    E. T. Schmidt
    Periodica Mathematica Hungarica, 2014, 69 : 32 - 40
  • [35] Slim Semimodular Lattices. I. A Visual Approach
    Gábor Czédli
    E. Tamás Schmidt
    Order, 2012, 29 : 481 - 497
  • [36] Slim Semimodular Lattices. I. A Visual Approach
    Czedli, Gabor
    Schmidt, E. Tamas
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2012, 29 (03): : 481 - 497
  • [37] Semimodular λ-lattices
    Chajda, Ivan
    Langer, Helmut
    JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING, 2022, 39 (01) : 79 - 96
  • [38] ON CONGRUENCE LATTICES OF LATTICES
    PUDLAK, P
    ALGEBRA UNIVERSALIS, 1985, 20 (01) : 96 - 114
  • [39] Diagrams and rectangular extensions of planar semimodular lattices
    Gábor Czédli
    Algebra universalis, 2017, 77 : 443 - 498
  • [40] Lamps in slim rectangular planar semimodular lattices
    Gábor Czédli
    Acta Scientiarum Mathematicarum, 2021, 87 : 381 - 413
12345