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  • CANCELLATIVE AND MALCEV PRESENTATIONS FOR FINITE REES INDEX SUBSEMIGROUPS AND EXTENSIONS

  • Part of
  • ALAN J. CAIN, EDMUND F. ROBERTSON, NIK RUŠKUC
  • Journal:
    Journal of the Australian Mathematical Society / Volume 84 / Issue 1 / February 2008
    Published online by Cambridge University Press:
    01 February 2008, pp. 39-61
    Print publication:
    February 2008
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  • 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.)