Minimal representations of a finite distributive lattice by principal congruences of a lattice

被引：0

作者：

Gratzer, George ^{[1
]}

Lakser, Harry ^{[2
]}

机构：

[1] Univ Manitoba, Winnipeg, MB R3T 2N2, Canada

[2] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

来源：

ACTA SCIENTIARUM MATHEMATICARUM | 2019年 / 85卷 / 1-2期

关键词：

finite lattice; principal congruence; ordered set;

D O I：

10.14232/actasm-017-060-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let the finite distributive lattice D be isomorphic to the congruence lattice of a finite lattice L. Let Q denote those elements of D that correspond to principal congruences under this isomorphism. Then Q contains 0, 1 is an element of D and all the join-irreducible elements of D. If Q contains exactly these elements, we say that L is a minimal representation of D by principal congruences of the lattice L. We characterize finite distributive lattices D with a minimal representation by principal congruences with the property that D has at most two dual atoms.

引用

页码：69 / 96

页数：28

共 15 条

[1] Representing a monotone map by principal lattice congruences [J].