An extension theorem for planar semimodular lattices

被引：0
作者：
G. Grätzer
E. T. Schmidt
机构：
[1] University of Manitoba,Department of Mathematics
[2] Mathematical Institute,undefined
[3] Budapest University of Technology and Economics,undefined
来源：
Periodica Mathematica Hungarica | 2014年 / 69卷
关键词：
Principal congruence; Order; Semimodular; Rectangular; Primary 06C10; Secondary 06B10;
D O I：
暂无
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学科分类号：
摘要：
We prove that every finite distributive lattice D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D$$\end{document} can be represented as the congruence lattice of a rectangular lattice K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K$$\end{document} in which all congruences are principal. We verify this result in a stronger form as an extension theorem.
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页码：32 / 40
页数：8
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