Axiomatizable and nonaxiomatizable congruence prevarieties
type: Item
instance of: scholarly article
title: Axiomatizable and nonaxiomatizable congruence prevarieties
zbMATH Open document ID: 1165.08002
author: Keith A. Kearnes
author: J. B. Nation
published in: Algebra Universalis
publication date: 2009-02-17T00:00:00Z
review text: For a variety \(V\), \(L(V)\) denotes the class of lattices embeddable in congruence lattices of algebras in \(V\). It is evident that \(L(V)\) is closed under \(I\), \(S\), and \(P\) and hence is a prevariety. If \(V\) satisfies any of the following conditions (a), (b), (c), then \(L(V)\) is first-order axiomatizable: (a) \(V\) is congruence distributive, (b) \(V\) is congruence \(n\)-permutable, (c) \(V\) contains a nontrivial finite strongly soluble algebra. The authors give some criteria for the first-order axiomatizability or nonaxiomatizability of \(L(V)\).
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08B05
zbMATH DE Number: 5508752
zbMATH Keywords: congruence prevariety
zbMATH Keywords: congruence identity
zbMATH Keywords: first-order axiomatizability
MaRDI profile type: Publication
full work available at URL: s00012-008-2068-y
OpenAlex ID: W2026119408
DOI: 10.1007/S00012-008-2068-Y
description: scientific article; zbMATH DE number 5508752