Affine complete varieties are congruence distributive
type: Item
instance of: scholarly article
title: Affine complete varieties are congruence distributive
zbMATH Open document ID: 0934.08007
author: Kalle Kaarli
author: Ralph McKenzie
published in: Algebra Universalis
publication date: 2000-02-27T00:00:00Z
review text: An algebra is affine complete if every function on \(A\) compatible with Con\(A\) is a polynomial over \(A\). A variety \(V\) is affine complete if all its members are. It is shown that every affine complete variety is congruence distributive and residually finite and a useful characterization of all arithmetical affine complete varieties of countable type is given. It is shown that affine complete varieties with finite residual bound have enough injectives and an example of an affine complete variety without finite residual bound is constructed. There are also several results concerning residually finite varieties whose finite members are congruence distributive.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08B10
Mathematics Subject Classification ID: 08B30
zbMATH DE Number: 1407080
zbMATH Keywords: affine complete variety
zbMATH Keywords: congruence distributivity
zbMATH Keywords: residual finiteness
MaRDI profile type: Publication
full work available at URL: s000120050058
OpenAlex ID: W2059599307
DOI: 10.1007/S000120050058
description: scientific article; zbMATH DE number 1407080