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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

Howie, J. M. (1964), ‘The maximum idempotent-separating congruence on an inverse semigroup’, Proc. Edinburgh Math. Soc. (2) 14, 71–79.Google Scholar
Howie, J. M. (1976), An introduction to semigroup theory (Academic Press, London).Google Scholar
Howie, J. M. (1981), ‘A class of bisimple idempotent-generated congruence-free semigroups’, Proc. Roy. Soc. Edinburgh A 88A, 169–184.Google Scholar
Liber, A. E. (1953), ‘On symmetric generalised groups’, Mat. Sb. 33 (75), 531–544 (in Russian).Google Scholar
Munn, W. D. (1974), ‘Congruence-free inverse semigroups’, Quart. J. Math. Oxford (Ser.) 25, 463–484.Google Scholar
Munn, W. D. (1975), ‘A note on congruence-free semigroups’, Quart. J. Math. Oxford (Ser.) 26, 385–387.Google Scholar
Sutov, E. G. (1960), ‘On semigroups of almost identical transformations’, Dokl. Akad. Nauk SSSR 134, 292–295 (in Russian).Google Scholar
Sutov, E. G. (1963), ‘Homomorphisms of the semigroup of all near-identity mappings’, Izv. Vysŝ. Učebn. Zaved. Matematika no. 2 (33), 176–180.Google Scholar