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On diagonal acts of monoids

Published online by Cambridge University Press:  17 April 2009

E. F. Robertson ,
N. Ruškuc  and
M. R. Thomson
E. F. Robertson
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland, United Kingdom, e-mail: edmund@mcs.st-and.ac.uk, nik@mcs.st-and.ac.uk, robertt@mcs.st-and.ac.uk
N. Ruškuc
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland, United Kingdom, e-mail: edmund@mcs.st-and.ac.uk, nik@mcs.st-and.ac.uk, robertt@mcs.st-and.ac.uk
M. R. Thomson
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland, United Kingdom, e-mail: edmund@mcs.st-and.ac.uk, nik@mcs.st-and.ac.uk, robertt@mcs.st-and.ac.uk
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Abstract

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It is proved that the monoid RN of all partial recursive functions of one variable is finitely generated, and that RN × RNis a cyclic (left and right) RN-act (under the natural diagonal actions s (a, b) = (sa, sb), (a, b) s = (as, bs)). We also construct a finitely presented monoid S such that S × S is a cyclic left and right S-act, and study further interesting properties of diagonal acts and their relationship with power monoids.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 167 - 175
Copyright
Copyright © Australian Mathematical Society 2001

References

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