Representing a monotone map by principal lattice congruences

被引：11

作者：

Czedli, G. ^{[1
]}

机构：

[1] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary

来源：

ACTA MATHEMATICA HUNGARICA | 2015年 / 147卷 / 01期

关键词：

principal congruence; lattice congruence; ordered set; order; poset; quasi-colored lattice; preordering; quasiordering; monotone map;

D O I：

10.1007/s10474-015-0539-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a lattice L, let Princ (L) denote the ordered set of principal congruences of L. In a pioneering paper, G. Gratzer proved that bounded ordered sets (in other words, posets with 0 and 1) are, up to isomorphism, exactly the Princ (L) of bounded lattices L. Here we prove that for each 0-separating boundpreserving monotone map psi between two bounded ordered sets, there are a lattice L and a sublattice K of L such that, in essence, psi is the map from Princ (K) to Princ (L) that sends a principal congruence to the congruence it generates in the larger lattice.

引用

页码：12 / 18

页数：7