Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T02:15:05.725Z Has data issue: false hasContentIssue false
  • English
  • Français

Automatic monoids and change of generators

Published online by Cambridge University Press:  01 November 1999

A. J. DUNCAN ,
E. F. ROBERTSON  and
N. RUšKUC
A. J. DUNCAN
Affiliation:
School of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne NE1 7RU; e-mail: [email protected]
E. F. ROBERTSON
Affiliation:
School of Mathematical and Computational Sciences, Mathematical Institute, University of St Andrews, The North Haugh, St Andrews, Fife KY16 9SS; e-mail: [email protected], e-mail: [email protected]
N. RUšKUC
Affiliation:
School of Mathematical and Computational Sciences, Mathematical Institute, University of St Andrews, The North Haugh, St Andrews, Fife KY16 9SS; e-mail: [email protected], e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The main result of this paper establishes invariance under change of generators for automatic structures for monoids (a property that is well known to hold for automatic groups but fails for semigroups). This result is then applied to show that if a free product of two monoids is automatic, then so are both the free factors. Finally, the difference between automatic structures, in terms of monoid generating sets and semigroup generating sets, is discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 3 , November 1999 , pp. 403 - 409
Copyright
© The Cambridge Philosophical Society 1999

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.)