Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T08:49:54.219Z Has data issue: false hasContentIssue false
  • English
  • Français

String rewriting and homology of monoids

Published online by Cambridge University Press:  01 June 1997

DANIEL E. COHEN
DANIEL E. COHEN
Affiliation:
Queen Mary and Westfield College, Mile End Rd., London E1 4NS. Email: d.e.cohen@qmw.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Results of Anick (1986), Squier (1987), Kobayashi (1990), Brown (1992b), and others, show that a monoid with a finite convergent rewriting system satisfies a homological condition known as FP∞.

In this paper we give a simplified version of Brown's proof, which is conceptual, in contrast with the other proofs, which are computational.

We also collect together a large number of results and examples of monoids and groups that satisfy FP∞ and others that do not. These may provide techniques for showing that various monoids do not have finite convergent rewriting systems, as well as explicit examples with which methods can be tested.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 7 , Issue 3 , June 1997 , pp. 207 - 240
Copyright
1997 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)