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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
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Abstract

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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