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Baer-Levi semigroups of partial transformations
Published online by Cambridge University Press: 17 April 2009
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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.
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- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 87 - 106
- Copyright
- Copyright © Australian Mathematical Society 2004
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