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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
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.
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- Research Article
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- Copyright
- Copyright © Australian Mathematical Society 1981
References
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