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.
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页码：121 / 127
页数：7
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