Three classes of orthomodular lattices

被引：11
|
作者：
Greechie, Richard J.
Legan, Bruce J. [1 ]
机构：
[1] Metropolitan State Univ, Dept Math, St Paul, MN 55106 USA
[2] Louisiana Tech Univ, Dept Math, Ruston, LA 71270 USA
来源：
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS | 2006年 / 45卷 / 02期
关键词：
orthomodular lattice (OML); commutator-finite OML; block-finite OML; locally finite OML; block extension property; weak block extension property; Greechie space; loop lemma; orthogonality space;
D O I：
10.1007/s10773-005-9022-y
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Let OML denote the class of all orthomodular lattices and C denote the class of those that are commutator-finite. Also, let C-1 denote the class of orthomodular lattices that satisfy the block extension property, C-2 those that satisfy the weak block extension property, and C-3 those that are locally finite. We show that the following strict containments hold: C subset of C1 subset of C2 subset of C3 subset of OML.
引用
收藏
页码：351 / 357
页数：7
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