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

页数：3

共 8 条

[1] A note on congruence lattices of slim semimodular lattices
Czedli, Gabor
[J]. ALGEBRA UNIVERSALIS, 2014, 72 (03) : 225 - 230
[2] Slim Semimodular Lattices. I. A Visual Approach
Czedli, Gabor
Schmidt, E. Tamas
[J]. ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2012, 29 (03): : 481 - 497
[3] Grätzer G, 2011, LATTICE THEORY: FOUNDATION, P1, DOI 10.1007/978-3-0348-0018-1
[4] Congruences of fork extensions of slim, planar, semimodular lattices
Gratzer, G.
[J]. ALGEBRA UNIVERSALIS, 2016, 76 (02) : 139 - 154
[5] Grätzer G, 2009, ACTA SCI MATH, V75, P29
[6] Gratzer G., 2016, CONGRUENCES FINITE L
[7] Grätzer G, 2007, ACTA SCI MATH, V73, P445
[8] On a result of Gabor Czedli concerning congruence lattices of planar semimodular lattices
Gratzer, George
[J]. ACTA SCIENTIARUM MATHEMATICARUM, 2015, 81 (1-2): : 25 - 32

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