A new look at the Jordan-Holder theorem for semimodular lattices

被引：24

作者：

Graetzer, G. ^{[1
]}

Nation, J. B. ^{[2
]}

机构：

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

[2] Univ Hawaiii, Honolulu, HI USA

来源：

ALGEBRA UNIVERSALIS | 2010年 / 64卷 / 3-4期

关键词：

semimodular lattice; maximal chain; finite length; congruence-determining sublattice;

D O I：

10.1007/s00012-011-0104-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that in a semimodular lattice L of finite length, from any prime interval we can reach any maximal chain C by an up- and a down-perspectivity. Therefore, C is a congruence-determining sublattice of L.

引用

页码：309 / 311

页数：3