Hostname: page-component-5cf477f64f-qls9x Total loading time: 0 Render date: 2025-04-03T22:55:22.381Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse semigroups with idempotents dually well-ordered

Part of: Semigroups Set theory

Published online by Cambridge University Press:  09 April 2009

A. Clement  and
F. Pastijn
A. Clement
Affiliation:
Dienst Hogere MeetkundeRijksuniversiteit GentKrijgslaan 281B-9000 Gent, Belgium
F. Pastijn
Affiliation:
Dienst Hogere MeetkundeRijksuniversiteit GentKrijgslaan 281B-9000 Gent, Belgium
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

All inverse semigroups with idempotents dually well-ordered may be constructed inductively. The techniques involved are the constructions of ordinal sums, direct limits and Bruck-Reilly extensions.

MSC classification

Secondary: 20M10: General structure theory 03E10: Ordinal and cardinal numbers
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 3 , December 1983 , pp. 373 - 385
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Feller, E. H. and Gantos, R. L., ‘Completely injective semigroups’, Pacific J. Math. 31 (1969), 359–366.CrossRefGoogle Scholar
[2]Hogan, J., ‘Bisimple semigroups with idempotents well-ordered’, Semigroup Forum 6 (1973), 298–316.CrossRefGoogle Scholar
[3]Howie, J. M., An introduction to semigroup theory (Academic Press, London, 1976).Google Scholar
[4]Kočin, B. P., ‘Structure of inverse ideally-simple ω-semigroups’, Vestnik Leningrad. Univ. Mat. 23, nr. 7 (1968), 41–50 (in Russian).Google Scholar
[5]Megyesi, L. and Pollák, G., ‘Uber die Struktur der Hauptidealhalbgruppen. I’, Acta Sci. Math. (Szeged) 29 (1968), 261–270.Google Scholar
[6]Megyest, L. and Pillák, G., ‘Uber die Struktur der Hauptidealhalbgruppen. II.’, Acta Sci. Math. (Szeged) 39 (1977), 103–108.Google Scholar
[7]Megyesi, L. and Pollák, G., ‘On simple principal ideal semigroups’, Studia Math., to appear.Google Scholar
[8]Munn, W. D., ‘Regular ω-semigroups’, Glasgow Math. J. (1968), 46–66.CrossRefGoogle Scholar
[9]Munn, W. D., personal communication.Google Scholar
[10]Petrich, M., Structrue of regular semigroups (Cahiers Mathématiques, Université des Sciences et Techniques du Languedoc, Montpellier, 1977).Google Scholar
[11]Reilly, N. R., ‘Bisimple w-semigroups’, Proc. Glasgow Math. Assoc 7 (1966), 160–167.CrossRefGoogle Scholar
[12]Sierpiński, W., Cardinal and ordinal numbers (Polish Scientific Publishers, Warszawa, 1965).Google Scholar
[13]Warne, R. J., ‘A class of bisimple inverse semigroups’, Pacific J. Math. 18 (1966), 563–577.CrossRefGoogle Scholar
[14]Warne, R. J., ‘Bisimple inverse semigroups mod groups’, Duke Math. J. 34 (1967), 787–812.CrossRefGoogle Scholar
[15]White, G. L., ‘The dual ordinal of a bisimple inverse semigroups’, Semigroup Forum 6 (1973), 295–297.CrossRefGoogle Scholar