Remarks on the Fraser-Horn property
type: Item
instance of: scholarly article
title: Remarks on the Fraser-Horn property
zbMATH Open document ID: 0605.08003
DOI: 10.1007/BF01190906
published in: Algebra Universalis
publication date: 1986-01-01T00:00:00Z
review text: A variety of algebras has the Fraser-Horn property (FHP) if all congruences of a direct product of two algebras are product congruences. A variety has definable principal congruences (DPC) if there exists a first order four-ary formula which describes the principal congruences. If this formula can be given as a (finite) set of equations, the variety has equationally definable principal congruences (EDPC). The important result of this short paper is that in any variety: \(EDPC=DPC+FHP\).
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 3977071
zbMATH Keywords: variety of algebras
zbMATH Keywords: Fraser-Horn property
zbMATH Keywords: product congruences
zbMATH Keywords: definable principal congruences
zbMATH Keywords: equationally definable principal congruences
author: Stanley N. Burris
reviewed by: Ervin Fried
MaRDI profile type: Publication
cites work: Q3934450
cites work: Congruence Relations in Direct Products
cites work: Uniform congruence schemes
description: scientific article; zbMATH DE number 3977071