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Congruences on semigroups generated by injective nilpotent transformations

Published online by Cambridge University Press:  17 April 2009

M. Paula O. Marques-Smith  and
R.P. Sullivan
M. Paula O. Marques-Smith
Affiliation:
Centro de Matematica, Universidade do Minho, 4710 Braga, Portugal
R.P. Sullivan
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Nedlands 6009, Australia
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In 1987, Sullivan characterised the elements of the semigroup NI(X) generated by the nilpotents in I(X), the symmetric inverse semigroup on an infinite set X; and, in the same year, Gomes and Howie did the same for finite X. In 1999, Marques-Smith and Sullivan determined all the ideals of NI(X) for arbitrary X. In this paper, we use that work to describe all the congruences on NI(X).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 3 , December 2006 , pp. 393 - 409
Copyright
Copyright © Australian Mathematical Society 2006

References

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