Description of commutative monoids over which all polygons are \(\omega\)-stable
type: Item
instance of: scholarly article
title: Description of commutative monoids over which all polygons are \(\omega\)-stable
zbMATH Open document ID: 0704.03018
DOI: 10.1007/BF01982014
author: V. S. Bogomolov
author: T. G. Mustafin
published in: Algebra and Logic
publication date: 1989-01-01T00:00:00Z
review text: A monoid \(S\) is called \(\omega\)-stabilizer [stabilizer, superstabilizer] if every left polygon over \(S\) has \(\omega\)-stable [stable, superstable] theory. Stabilizers and superstabilizers were characterized by \textit{T. G. Mustafin} [Transl., Ser. 2, Am. Math. Soc. 195, 205--223 (1999); translation from Tr. Inst. Mat. 8, 92--108 (1988; Zbl 0725.03019)]. In this paper the following theorem is proved. A countable commutative monoid \(S\) is an \(\omega\)-stabilizer if and only if \(S\) is an abelian group with finite or countable number of subgroups, or \(S\) is a finite monoid with a unique proper ideal.
Mathematics Subject Classification ID: 03C65
Mathematics Subject Classification ID: 03C45
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 03C15
zbMATH DE Number: 4154420
zbMATH Keywords: \(\omega \)-stable theory
zbMATH Keywords: polygon over monoid
zbMATH Keywords: \(\omega \)-stabilizer
zbMATH Keywords: commutative monoid
MaRDI profile type: Publication
cites work: Q4700629
cites work: Q5652898
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description: scientific article; zbMATH DE number 4154420