On regular and regularized varieties
type: Item
instance of: scholarly article
title: On regular and regularized varieties
zbMATH Open document ID: 0619.08004
DOI: 10.1007/BF01230618
published in: Algebra Universalis
publication date: 1986-01-01T00:00:00Z
review text: Let V be an irregular variety defined by a set of regular identities and an identity of the form \(t(x,y)=t(x,z)\). (Any irregular variety can be defined in such a way.) A variety \(\bar V\) containing the regularization of V is introduced and studied. It has the following properties. \(\bar V\) is finitely based if V is. Every algebra from \(\bar V\) is a coherent Lallement sum (this is a generalization of a Płonka sum) of algebras from V. There is a theorem characterizing the structure of algebras in \(\bar V\) by means of some special coherent Lallement sums. Some sufficient conditions are given implying that the regularization of an irregular variety consists of Płonka sums only. The last section deals with equational bases for regularized varieties.
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 08B25
zbMATH DE Number: 4004247
zbMATH Keywords: irregular variety
zbMATH Keywords: regular identities
zbMATH Keywords: regularization
zbMATH Keywords: coherent Lallement sums
zbMATH Keywords: Płonka sums
zbMATH Keywords: equational bases
zbMATH Keywords: regularized varieties
author: Anna Romanowska
reviewed by: Jaroslav Ježek
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01230618
OpenAlex ID: W1992285743
description: scientific article; zbMATH DE number 4004247