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Division theorems for inverse and pseudo-inverse semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

F. Pastijn
F. Pastijn
Affiliation:
Dienst Hogere Meetkunde, Rijksuniversiteit te Gent, Krijgslaan 271, B-9000 Gent, Belgium
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Abstract

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We show that every inverse semigroup is an idempotent separating homomorphic image of a convex inverse subsemigroup of a P-semigroup P(G, L, L), where G acts transitively on L. This division theorem for inverse semigroups can be applied to obtain a division theorem for pseudo-inverse semigroups.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 4 , December 1981 , pp. 415 - 420
Copyright
Copyright © Australian Mathematical Society 1981

References

Chen, S. Y. and Hsieh, S. c. (1974), ‘Factorizable inverse semigroups’, Semigroup Forum 8, 283–297.CrossRefGoogle Scholar
Howie, J. M. (1976), An introduction to semigroup theory (Academic Press, London).Google Scholar
McAlister, D. B. (1974a), ‘Groups, semilattices and inverse semigroups’, Trans. Amer. Math. Soc. 192, 227–244.Google Scholar
McAlister, D. B. (1974b), ‘Groups, semilattices and inverse semigroups II’, Trans. Amer. Math. Soc., 196, 351–369.CrossRefGoogle Scholar
McAlister, D. B. (1978), ‘E-unitary inverse semigroups over semilattices’, Glasgow Math. J. 19, 1–12.CrossRefGoogle Scholar
O'Carroll, L. (1974), ‘A note on free inverse semigroups’, Proc. Edinburgh Math. Soc. (2) 19, 17–23.CrossRefGoogle Scholar
O'Carroll, L. (1976), ‘Embedding theorems for proper inverse semigroups’, J. Algebra 42, 26–40.CrossRefGoogle Scholar
Pastijn, F. (1980), ‘Semilattices with a transitive automorphism group’, J. Austral. Math. Soc. Ser. A 29, 29–34.CrossRefGoogle Scholar
Pastijn, F. (a), ‘Rectangular bands of inverse semigroups’, preprint.Google Scholar
Pastijn, F. (b), ‘The structure of pseudo-inverse semigroups’, preprint.Google Scholar
Reilly, N. R. and Munn, W. D. (1976), ‘E-unitary congruences on inverse semigroups’, Glasgow Math. J. 17, 57–75.CrossRefGoogle Scholar