Lattices of quotients of completely distributive lattices

被引：4

作者：

He, W ^{[1
]}

Luo, MK

机构：

[1] Nanjing Normal Univ, Dept Math, Nanjing 210097, Peoples R China

[2] Sichuan Univ, Dept Math, Chengdu 610064, Peoples R China

来源：

ALGEBRA UNIVERSALIS | 2005年 / 54卷 / 01期

基金：

中国国家自然科学基金;

关键词：

quotient lattice; completely distributive;

D O I：

10.1007/s00012-005-1932-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the complete lattice Q(L) of all quotients of a completely distributive lattice L. We show that Q(L) is not a completely distributive lattice even for L a completely distributive algebraic lattice. Some necessary and sufficient conditions for Q(L) to be a completely distributive lattice are given.

引用

页码：121 / 127

页数：7

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