Lexicographic products of ordered sets and lattices

被引：0

作者：

Lee, JG ^{[1
]}

机构：

[1] Sogang Univ, Dept Math, Seoul 121742, South Korea

来源：

HOUSTON JOURNAL OF MATHEMATICS | 1997年 / 23卷 / 04期

关键词：

lexicographic product; height; ranked; ordered set; bounded; lattice;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we are concerned with lexicographic products of ordered sets, which are much more complicated than lexicographic sums of ordered sets. We show that the lexicographic product of ranked ordered sets over a finite ordered sat is ranked, and we actually compute the height of every element in the lexicographic product of arbitrary ordered sets of finite length over a finite ordered set. Moreover, we give a necessary and sufficient condition for the lexicographic product of (distributive, modular) lattices over a well-founded set to be a (distributive, modular) lattice.

引用

页码：591 / 601

页数：11