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Baer-Levi semigroups of partial transformations

Published online by Cambridge University Press:  17 April 2009

Fernanda A. Pinto  and
R.P. Sullivan
Fernanda A. Pinto
Affiliation:
Centro de Matematica, Universidade do Minho, 4710 Braga, Portugal
R.P. Sullivan
Affiliation:
School of Mathematics & Statistics, University of Western Australia, Nedlands W.A. 6009, Australia
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Let X be an infinite set and suppose א0 ≤ q ≤ |X|. The Baer-Levi semigroup on X is the set of all injective ‘total’ transformations α: X → X such that |X\Xα| = q. It is known to be a right simple, right cancellative semigroup without idempotents, its automorphisms are “inner”, and some of its congruences are restrictions of Malcev congruences on I(X), the symmetric inverse semigroup on X. Here we consider algebraic properties of the semigroup consisting of all injective ‘partial’ transformations α of X such that |X\Xα| = q: in particular, we descried the ideals and Green's relations of it and some of its subsemigroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 87 - 106
Copyright
Copyright © Australian Mathematical Society 2004

References

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