Finite axiomatizability of congruence rich varieties
type: Item
instance of: scholarly article
title: Finite axiomatizability of congruence rich varieties
zbMATH Open document ID: 0840.08010
DOI: 10.1007/BF01204782
author: George F. McNulty
author: Jaroslav Ježek
published in: Algebra Universalis
publication date: 1995-11-22T00:00:00Z
review text: The notion of a congruence rich variety of algebras is introduced. A variety \(V\) is said to be congruence rich if for each positive integer \(n\) there is a positive integer \(m\) such that every finitely generated algebra in \(V\) with more than \(n\) elements has a homomorphic image with more than \(n\) elements but no more than \(m\) elements. There are examples of varieties of this kind: any finitely generated congruence modular variety and any variety of directoids (introduced in a paper of the first author and \textit{R. Quackenbush} [Algebra Univers. 27, 49-69 (1990; Zbl 0699.08002)]). The question whether locally finite subvarieties of a congruence rich variety are relatively finitely based is discussed. The results obtained are applied to prove that some interesting five-element directoid is not finitely based but fails to be inherently nonfinitely based.
Mathematics Subject Classification ID: 08B99
Mathematics Subject Classification ID: 08B10
Mathematics Subject Classification ID: 08C10
zbMATH DE Number: 819274
zbMATH Keywords: relatively finitely based variety
zbMATH Keywords: congruence rich variety
zbMATH Keywords: locally finite subvarieties
zbMATH Keywords: directoid
MaRDI profile type: Publication
cites work: Finite equational bases for finite algebras in a congruence-distributive equational class
cites work: Q3832626
cites work: Q3934450
cites work: Residually Small Varieties with Modular Congruence Lattices
cites work: An inherently nonfinitely based commutative directoid
cites work: Q3490146
cites work: Nonfinitely based three-element idempotent groupoids
cites work: Directoids: Algebraic models of up-directed sets
cites work: Inherently Nonfinitely Based Solvable Algebras
cites work: Identities satisfied by a finite ring
cites work: Identities in Finite Algebras
cites work: Equational Bases for Lattice Theories.
cites work: A new product of algebras and a type reduction theorem
cites work: Finite equational bases for congruence modular varieties
cites work: TARSKI’S FINITE BASIS PROBLEM IS UNDECIDABLE
cites work: Identical relations in finite groups
cites work: Basic questions for general algebras
cites work: INHERENTLY NONFINITELY BASED FINITE SEMIGROUPS
cites work: Q4283158
description: scientific article; zbMATH DE number 819274