A note on congruence lattices of slim semimodular lattices

被引：10
|
作者：
Czedli, Gabor [1 ]
机构：
[1] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary
来源：
ALGEBRA UNIVERSALIS | 2014年 / 72卷 / 03期
关键词：
rectangular lattice; planar lattice; semimodular lattice; congruence lattice;
D O I：
10.1007/s00012-014-0286-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Recently, G. Gratzer has raised an interesting problem: Which distributive lattices are congruence lattices of slim semimodular lattices? We give an eight element slim distributive lattice that cannot be represented as the congruence lattice of a slim semimodular lattice. Our lattice demonstrates the difficulty of the problem.
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页码：225 / 230
页数：6
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