Semigroups with one defining relation whose elementary theories are solvable
type: Item
instance of: scholarly article
title: Semigroups with one defining relation whose elementary theories are solvable
zbMATH Open document ID: 0549.20036
DOI: 10.1007/BF00968793
author: Yu. M. Vazhenin
published in: Siberian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: A semigroup with one defining relation has a decidable elementary theory iff it is either monogenic or generated by two elements a,b and defined by one of the following relations: (I) \(ab=ba\), (II) \(ab=b^ k\), \(k=1,2,...\), (III) \(ba=b^ k\), \(k=1,2,...\), (IV) \(ab=aba\), (V) \(ba=aba\), (VI) \(ab=bab^ 2\), (VII) \(ba=b^ 2ab\), (VIII) \(a=bab\), (IX) \(a^ 2=b^ 2\).
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 03B25
zbMATH DE Number: 3875541
zbMATH Keywords: semigroup
zbMATH Keywords: defining relation
zbMATH Keywords: decidable elementary theory
zbMATH Keywords: relations
reviewed by: Jaak Henno
MaRDI profile type: Publication
cites work: Q4170913
cites work: Sur la liaison entre problèmes combinatoires et algorithmiques
cites work: Q5641547
full work available at URL: https://doi.org/10.1007/bf00968793
OpenAlex ID: W2039633928
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description: scientific article; zbMATH DE number 3875541