Subdirect products of hereditary congruence lattices

被引：3

作者：

Snow, JW ^{[1
]}

机构：

[1] Sam Houston State Univ, Dept Math & Stat, Huntsville, TX 77341 USA

来源：

ALGEBRA UNIVERSALIS | 2005年 / 54卷 / 01期

关键词：

congruence lattice; primitive positive formula; hereditary congruence lattice;

D O I：

10.1007/s00012-005-1922-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A congruence lattice L of an algebra A is called power-hereditary if every 0-1 sublattice of L-n is the congruence lattice of an algebra on A(n) for all positive integers n. Let A and B be finite algebras. We prove center dot If ConA is distributive, then every subdirect product of ConA and ConB is a congruence lattice on A x B. center dot If ConA is distributive and ConB is power- hereditary, then (ConA) x(ConB) is power-hereditary. center dot If ConA congruent to N-5 and ConB is modular, then every subdirect product of ConA and ConB is a congruence lattice. center dot Every congruence lattice representation of N-5 is power-hereditary.

引用

页码：65 / 71

页数：7