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Generators and relations of Rees matrix semigroups

Published online by Cambridge University Press:  20 January 2009

H. Ayik  and
N. Ruškuc
H. Ayik
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews Ky16 9SS, Scotland, E-mail address: ayik@dcs.st-and.ac.uk, nik@dcs.st-and.ac.uk
N. Ruškuc
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews Ky16 9SS, Scotland, E-mail address: ayik@dcs.st-and.ac.uk, nik@dcs.st-and.ac.uk
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In this paper we consider finite generation and finite presentability of Rees matrix semigroups (with or without zero) over arbitrary semigroups. The main result states that a Rees matrix semigroup M[S; I, J; P] is finitely generated (respectively, finitely presented) if and only if S is finitely generated (respectively, finitely presented), and the sets I, J and S\U are finite, where U is the ideal of S generated by the entries of P.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 3 , October 1999 , pp. 481 - 495
Copyright
Copyright © Edinburgh Mathematical Society 1999

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