Mal'tsev products of varieties. I
type: Item
instance of: scholarly article
title: Mal'tsev products of varieties. I
zbMATH Open document ID: 1497.08004
author: Tomasz Penza
author: Anna Romanowska
published in: Algebra Universalis
publication date: 2021-05-06T00:00:00Z
review text: Let \(\mathcal{V}\) and \(\mathcal{W}\) be varieties of algebras of the same similarity type, with no nullary operations. The Mal'tsev product \(\mathcal{V}\circ\mathcal{W}\) is a \textit{quasivariety} that consists of algebras with a congruence \(\theta\) such that the quotient \(A^\theta\) is in \(\mathcal{W}\) and each \(\theta\)-class \(a^\theta\) is in \(\mathcal{V}\). This paper describes the identities true in \(\mathcal{V}\circ\mathcal{W}\) in terms of the identities satisfied in \(\mathcal{V}\) and \(\mathcal{W}\) (Section 2). The main result (Theorem 3.3.) provides a new sufficient condition for \(\mathcal{V}\circ\mathcal{W}\) to be a variety. Finally, in Section 4, applications of this result are presented for \(\mathcal{W}\) being the variety of different kinds of generalizations of idempotent semigroups.
reviewed by: Anna Zamojska-Dzienio
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 7345065
zbMATH Keywords: Mal'tsev product
zbMATH Keywords: equational base
zbMATH Keywords: variety
zbMATH Keywords: quasivariety
MaRDI profile type: Publication
full work available at URL: s00012-021-00721-w
OpenAlex ID: W3158783823
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DOI: 10.1007/S00012-021-00721-W
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description: scientific article; zbMATH DE number 7345065