The variety of Kleene algebras with conversion is not finitely based
type: Item
instance of: scholarly article
title: The variety of Kleene algebras with conversion is not finitely based
zbMATH Open document ID: 0954.08004
DOI: 10.1016/S0304-3975(99)00079-1
author: Siniša Crvenković
author: Igor Dolinka
author: Zoltán Ésik
published in: Theoretical Computer Science
publication date: 2000-06-04T00:00:00Z
review text: The elements of the full Kleene algebra (with conversion) of a set \(A\) are the binary relations on \(A\), and the operations are those of forming unions, compositions, reflexive, transitive closures and converses of relations. Moreover, the empty relation and the identity relation on \(A\) are included as constants. The variety \(KA^\vee\) generated by all such relation algebras is the variety of Kleene algebras. The variety \(KA\) of conversion-free Kleene algebras is obtained similarly by omitting the conversion operation from the relation algebras. It is known that the equational theory of the variety \(KA\) is not finitely based. In this paper the authors prove in two different ways that the same holds for the variety \(KA^\vee\).
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 68Q45
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 08A02
Mathematics Subject Classification ID: 08A70
zbMATH DE Number: 1454291
zbMATH Keywords: binary relations
zbMATH Keywords: relation algebras
zbMATH Keywords: variety of Kleene algebras
zbMATH Keywords: equational theory
reviewed by: Magnus Steinby
MaRDI profile type: Publication
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full work available at URL: s0304-3975(99)00079-1
OpenAlex ID: W1986949269
description: scientific article; zbMATH DE number 1454291