Fraser-Horn identities can be written in two variables
type: Item
instance of: scholarly article
title: Fraser-Horn identities can be written in two variables
zbMATH Open document ID: 0669.08003
DOI: 10.1007/BF01236861
published in: Algebra Universalis
publication date: 1989-01-01T00:00:00Z
review text: A Mal'cev condition for varieties with directly decomposable congruences (DDC) was given by \textit{G. A. Fraser} and \textit{A. Horn} [Proc. Am. Math. Soc. 26, 390-394 (1970; Zbl 0241.08004)]. The identities they used involved three variables, being built up from binary, ternary, and \(m+1\)- ary terms. This paper provides a system of identities involving only two variables, being built up from binary and \(m+2\)-ary terms. As a consequence of this we have the result that a variety \({\mathcal V}\) has DDC if and only if \(F_{{\mathcal V}}(2)\times F_{{\mathcal V}}(2)\) has DDC.
Mathematics Subject Classification ID: 08B05
zbMATH DE Number: 4095534
zbMATH Keywords: Mal'cev condition for varieties with directly decomposable congruences
zbMATH Keywords: identities
author: Jaromír Duda
reviewed by: Sheila Oates-Williams
MaRDI profile type: Publication
cites work: Q3666905
cites work: Varieties having directly decomposable congruence classes
cites work: Q3731651
cites work: Congruence Relations in Direct Products
full work available at URL: https://doi.org/10.1007/bf01236861
OpenAlex ID: W2067122051
description: scientific article; zbMATH DE number 4095534