On the behaviour of congruence-functors
type: Item
instance of: scholarly article
title: On the behaviour of congruence-functors
zbMATH Open document ID: 0645.08005
DOI: 10.1007/BF01188396
published in: Algebra Universalis
publication date: 1987-01-01T00:00:00Z
review text: Let Comp \({\mathfrak A}\) be the semilattice of all compact congruences of the algebra \({\mathfrak A}\). Any homomorphisms \(\phi\) : \({\mathfrak A}\to {\mathfrak B}\) of algebras of a variety K induces a homomorphism Comp \(\phi\) by the identity (Comp \(\phi)\)(\(\Theta)\)(a,a')\(=\Theta (\phi (a),\phi (a'))\). It is proved that the functor Comp has the following properties: it preserves products iff the principal congruences can be defined in K by a finite set of equations; it always preserves surjectivity; it preserves injectivity iff K satisfies the Congruence Extension Property; it preserves products and injectivity iff the equation above contains only the four elements which are involved in the congruence; it never preserves coproducts.
Mathematics Subject Classification ID: 08B30
Mathematics Subject Classification ID: 08B25
Mathematics Subject Classification ID: 08A45
zbMATH DE Number: 4051704
zbMATH Keywords: compact congruences
zbMATH Keywords: products
zbMATH Keywords: surjectivity
zbMATH Keywords: injectivity
zbMATH Keywords: Congruence Extension Property
zbMATH Keywords: coproducts
author: Ervin Fried
reviewed by: Ernest Płonka
MaRDI profile type: Publication
cites work: A note on the congruence extension property
cites work: Uniform congruence schemes
full work available at URL: https://doi.org/10.1007/bf01188396
OpenAlex ID: W1994823439
description: scientific article; zbMATH DE number 4051704