A characterization of varieties.
type: Item
instance of: scholarly article
title: A characterization of varieties.
zbMATH Open document ID: 1058.08011
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: Let \(\mathcal L\) be a language of algebras and \(K\) a quasivariety of \(\mathcal L\)-algebras. Let \(\mathcal A\) be an \(\mathcal L\)-algebra. A congruence \(\Theta \in \text{Con} \mathcal A\) is called a \(K\)-congruence if \(\mathcal A / \Theta \in K\). The set \(\text{Con}_K \mathcal A\) of all \(K\)-congruences forms an algebraic lattice which is a meet-complete subsemilattice of \(\text{Con} \mathcal A\). The author proves that \(K\) is a variety if \(\text{Con}_K \mathcal A\) is a sublattice of \(\text{Con} \mathcal A\) for all \(\mathcal A \in K\).
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08C15
zbMATH DE Number: 2158726
zbMATH Keywords: quasivariety
zbMATH Keywords: relative congruence
author: J. G. Raftery
MaRDI profile type: Publication
full work available at URL: s000120050225
OpenAlex ID: W2084181723
DOI: 10.1007/S000120050225
description: scientific article; zbMATH DE number 2158726