Relative principal congruences in congruence-modular quasivarieties
type: Item
instance of: scholarly article
title: Relative principal congruences in congruence-modular quasivarieties
zbMATH Open document ID: 0933.08004
author: Janusz Czelakowski
published in: Algebra Universalis
publication date: 2000-02-27T00:00:00Z
review text: For a quasivariety \(Q\) of type \(\tau \) and an algebra \(A\) of the same type, \(\text{Con}_QA\) is defined to be the lattice of all congruences \(\theta \) on \(A\) such that \(A/\theta \in Q\). The members of \(\text{Con}_QA\) are called relative congruences. The concept of relative congruence modularity for quasivarieties is introduced in the paper (it is equivalent to the condition that the lattice \(\text{Con}_QF(\omega)\) is modular, where \(F(\omega)\) is the free algebra of \(Q\) with countable many generators). In any quasivariety relative principal congruences are defined by means of a possibly infinite disjunction of existentially parametrized conjunctions of finite sets of equations; this property is denoted by LEDPC with respect to the family \(P\) of finite set of equations. A quasivariety \(Q\) has equationally definable relative principal congruences iff \(Q\) has LEDPC with respect to a one-element family. The purpose of the paper is to study the relationship between the LEDPC and relative congruence modularity.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 08B05
zbMATH DE Number: 1407091
zbMATH Keywords: quasivariety
zbMATH Keywords: relative congruence modularity
zbMATH Keywords: equational definability of congruences
MaRDI profile type: Publication
full work available at URL: s000120050069
OpenAlex ID: W2023583272
DOI: 10.1007/S000120050069
description: scientific article; zbMATH DE number 1407091