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

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