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.
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