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A congruence-free inverse semigroup associated with a pair of infinite cardinals

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

J. M. Howie
J. M. Howie
Affiliation:
Mathematical Institute, University of St. Andrews, Scotland
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Abstract

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Let m, n be infinite cardinals such that m < n, and let X be a set of cardinality m. Within the symmetric inverse semigroup on X the elements whose domain and range have complements of cardinality m form an inverse semigroup T. The closure Eω of the semilattice E of idempotents of T is a fundamental bismple inverse semigroup. Its maximum congruence is described. The quotient of Eο by this maximum congruence is a bisimple, congruence is a bisimple, congruence-free inverse semigroup.

MSC classification

Secondary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 3 , October 1981 , pp. 337 - 342
Copyright
Copyright © Australian Mathematical Society 1981

References

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