Quasi-identities of finite semigroups and symbolic dynamics
type: Item
instance of: scholarly article
title: Quasi-identities of finite semigroups and symbolic dynamics
zbMATH Open document ID: 0840.20062
DOI: 10.1007/BF02762086
author: S. W. Margolis
author: Mark Sapir
published in: Israel Journal of Mathematics
publication date: 1996-02-12T00:00:00Z
review text: An algebra is called inherently non-finitely \((Q-)\) based if it is not contained in any locally finite and finitely based (quasi-)variety. \textit{M. V. Sapir} first proved that there exist finite inherently non-finitely based semigroups [Izv. Akad. Nauk SSSR, Ser. Mat. 51, No. 2, 319-340 (1987; Zbl 0646.20047)]\ and then effectively described them all [Mat. Sb., Nov. Ser. 133, 154-166 (1987; Zbl 0634.20027)]. In the paper under review the authors show that, in strong contrast with the variety case, no finite semigroup is inherently non-finitely \(Q\)-based. The proof makes essential use of the connection between Burnside type problems for semigroups and symbolic dynamics established in the first of the cited papers by M. V. Sapir.
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 836171
zbMATH Keywords: quasi-identity
zbMATH Keywords: locally finite semigroups
zbMATH Keywords: Zimin word
zbMATH Keywords: uniformly recurrent words
zbMATH Keywords: irreducible words
zbMATH Keywords: finite inherently non-finitely based semigroups
zbMATH Keywords: Burnside type problems for semigroups
zbMATH Keywords: symbolic dynamics
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02762086
OpenAlex ID: W2005617286
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description: scientific article; zbMATH DE number 836171