Whaley's Theorem for Finite Lattices

被引：0
|
作者：
Ralph Freese
Jennifer Hyndman
J. B. Nation
机构：
[1] University of Hawaii,Department of Mathematics
来源：
Order | 2003年 / 20卷 / 3期
关键词：
lattice; ordered set; sublattice; maximal sublattice;
D O I：
10.1023/B:ORDE.0000026464.36426.09
中图分类号：
学科分类号：
摘要：
Whaley's Theorem on the existence of large proper sublattices of infinite lattices is extended to ordered sets and finite lattices. As a corollary it is shown that every finite lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|1/3. It is also shown that that every finite modular lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|1/2, and every finite distributive lattice L with |L|≥4 contains a proper sublattice S with |S|≥3/4|L|.
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收藏
页码：223 / 228
页数：5
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