A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier)
type: Item
instance of: scholarly article
title: A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier)
zbMATH Open document ID: 0832.20080
DOI: 10.1016/0022-4049(94)00043-I
author: Yves Lafont
published in: Journal of Pure and Applied Algebra
publication date: 1995-07-03T00:00:00Z
review text: The paper deals with Squier's arguments on finite derivation type [\textit{C. C. Squier}, J. Pure Appl. Algebra 49, 201-217 (1987; Zbl 0648.20045); \textit{C. C. Squier} and \textit{F. Otto}, Lect. Notes Comput. Sci. 256, 74-82 (1987; Zbl 0625.03023)]. Proofs are made shorter and easier by categorical machinery. Squier's finiteness condition is of invariant type. It can be defined in terms of a finite presentation, but does not depend on the choice of this presentation. The result is that if a monoid has finite derivation type, then its third homology group is of finite type.
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M35
Mathematics Subject Classification ID: 20M50
zbMATH DE Number: 762340
zbMATH Keywords: finite derivation type
zbMATH Keywords: finiteness condition
zbMATH Keywords: finite presentation
zbMATH Keywords: monoid
zbMATH Keywords: homology group
reviewed by: Georgiy E. Tseytlin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 762340