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The ideal structure of nilpotent-generated transformation semigroups

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, 4700 Braga, Portugal
R.P. Sullivan
Affiliation:
Department of Mathematics and Statistics, Sultanb Qaboos University, Oman and Department of Mathematics, University of Western Australia, Nedlands WA 6907, Australia
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In 1987 Sullivan determined the elements of the semigroup N(X) generated by all nilpotent partial transformations of an infinite set X; and later in 1997 he studied subsemigroups of N(X) defined by restricting the index of the nilpotents and the cardinality of the set. Here, we describe the ideals and Green's relations on such semigroups, like Reynolds and Sullivan did in 1985 for the semigroup generated by all idempotent total transformations of X. We then use this information to describe the congruences on certain Rees factor semigroups and to construct families of congruence-free semigroups with interesting algebraic properties. We also study analogous questions for X finite and for one-to-one partial transformations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 2 , October 1999 , pp. 303 - 318
Copyright
Copyright © Australian Mathematical Society 1999

References

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