On the relationship of AP, RS and CEP in congruence modular varieties
type: Item
instance of: scholarly article
title: On the relationship of AP, RS and CEP in congruence modular varieties
zbMATH Open document ID: 0608.08003
DOI: 10.1007/BF01224023
author: Clifford Bergman
published in: Algebra Universalis
publication date: 1986-01-01T00:00:00Z
review text: The main result is that a congruence modular variety has the congruence extension property provided it is residually small, has the amalgamation property, a free algebra on four generators with congruence lattice of finite length, and its subdirectly irreducibles satisfy two commutator identities (C2) and (R) valid in the distributive case.
Mathematics Subject Classification ID: 08B10
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 3983245
zbMATH Keywords: congruence modular variety
zbMATH Keywords: congruence extension property
zbMATH Keywords: residually small
zbMATH Keywords: amalgamation property
zbMATH Keywords: free algebra
zbMATH Keywords: congruence lattice of finite length
zbMATH Keywords: subdirectly irreducibles
zbMATH Keywords: commutator identities
Wikidata QID: Q60143378
reviewed by: Christian Herrmann
MaRDI profile type: Publication
cites work: Amalgamation classes of some distributive varieties
cites work: Q3934450
cites work: A note on the congruence extension property
cites work: Q3775604
cites work: Residually Small Varieties with Modular Congruence Lattices
cites work: An easy way to the commutator in modular varieties
cites work: A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity
cites work: Injectivity and related concepts in modular varieties: II. The congruence extension property
cites work: Injectivity and congruence extension property in congruence distributive equational classes
cites work: Narrowness implies uniformity
cites work: Q3853703
cites work: Residually small varieties
full work available at URL: https://doi.org/10.1007/bf01224023
OpenAlex ID: W3023642164
description: scientific article; zbMATH DE number 3983245