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CANCELLATIVE AND MALCEV PRESENTATIONS FOR FINITE REES INDEX SUBSEMIGROUPS AND EXTENSIONS

Part of: Semigroups

Published online by Cambridge University Press:  01 February 2008

ALAN J. CAIN
Affiliation:
School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK (email: alanc@mcs.st-and.ac.uk)
EDMUND F. ROBERTSON
Affiliation:
School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK (email: edmund@mcs.st-and.ac.uk)
NIK RUŠKUC
Affiliation:
School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK (email: nik@mcs.st-and.ac.uk)
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Abstract

It is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, cancellative, left-cancellative and right-cancellative presentations. (A Malcev (respectively, cancellative, left-cancellative, right-cancellative) presentation is a presentation of a special type that can be used to define any group-embeddable (respectively, cancellative, left-cancellative, right-cancellative) semigroup.)

Type
Research Article
Copyright
Copyright © 2008 Australian Mathematical Society

References

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CANCELLATIVE AND MALCEV PRESENTATIONS FOR FINITE REES INDEX SUBSEMIGROUPS AND EXTENSIONS
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