Lyndon's groupoid is not inherently nonfinitely based
type: Item
instance of: scholarly article
title: Lyndon's groupoid is not inherently nonfinitely based
zbMATH Open document ID: 0703.08005
DOI: 10.1007/BF01182458
author: Tamás Bajusz
author: Ágnes Szendrei
author: George F. McNulty
published in: Algebra Universalis
publication date: 1990-01-01T00:00:00Z
review text: The first example of a finite algebra which does not have a finite basis for its laws was given by \textit{R. C. Lyndon} [Proc. Am. Math. Soc. 5, 8-9 (1954; Zbl 0055.027)]. Since then, other examples have been given, many of which have been inherently nonfinitely based, that is, have not belonged to any locally finite finitely based variety. The question naturally arises as to whether Lyndon's algebra \({\mathbb{L}}\) is inherently nonfinitely based. In this paper it is shown that it is not, by exhibiting a finitely based finite algebra \({\mathbb{B}}\) of which \({\mathbb{L}}\) is a subalgebra. \{The same result was given by the second author and \textit{C. R. Shallon} [Lect. Notes Math. 1004, 206-231 (1983; Zbl 0513.08003)] but, unfortunately, there was an error in their proof.\}
Mathematics Subject Classification ID: 08B05
zbMATH DE Number: 4152447
zbMATH Keywords: Lyndon's algebra
zbMATH Keywords: inherently nonfinitely based
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4152447