Hostname: page-component-cb9f654ff-d5ftd Total loading time: 0 Render date: 2025-09-01T02:29:21.028Z Has data issue: false hasContentIssue false
  • English
  • Français

On bisimple semigroups generated by a finite number of idempotents

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Karl Byleen
Karl Byleen
Affiliation:
Department of Mathematics, Statistics, and Computer Science Marquette UniversityMilwaukee, Wisconsin 53233, U.S.A.
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.

Non-completely simple bisimple semigroups S which are generated by a finite number of idempotents are studied by means of Rees matrix semigroups over local submonoids eSe, e = e2 ∈ S. If under the natural partial order on the set Es of idempotents of such a semigroup S the sets ω(e) = {ƒ ∈ Es: ƒ ≤ e} for each e ∈ Es are well-ordered, then S is shown to contain a subsemigroup isomorphic to Sp4, the fundamental four-spiral semigroup. A non-completely simple hisimple semigroup is constructed which is generated by 5 idempotents but which does not contain a subsemigroup isomorphic to Sp4.

MSC classification

Secondary: 20M10: General structure theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 1 , August 1982 , pp. 92 - 101
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Allen, D. Jr, ‘A generalization of the Rees theorem to a class of regular semigroups’, Semigroup Forum 2 (1971), 321–331.CrossRefGoogle Scholar
[2]Byleen, K., ‘Regular four-spiral semigroups, idempotent-generated semigroups and the Rees construction’, Semigroup Forum 22 (1981), 97–100.Google Scholar
[3]Byleen, K., Meakin, J. and Pastijn, F., ‘The fundamental four-spiral semigroup’, J. Algebra 54 (1978), 6–26.CrossRefGoogle Scholar
[4]Byleen, K., Meakin, J. and Pastijn, F., ‘Building bisimple idempotent-generated semigroups’. J. Algebra 65 (1980), 60–83.CrossRefGoogle Scholar
[5]Hogan, J. W., ‘Bisimple semigroups with idempotents well-ordered’. Semigroup Forum 6 (1973), 298–316.Google Scholar
[6]McAlister, D. B., ‘Groups, semilattices and inverse semigroups’, Trans. Amer. Math. Soc. 192 (1974), 227–244.Google Scholar
[7]McAlister, D. B., ‘Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups’. J. Austral. Math. Soc., Ser A 31 (1981), 325–336.Google Scholar
[8]McAlister, D. B. and McFadden, R. (editors), Proceedings of the Svniposium on Regular Semigroups, (Northern Illinois University, DeKalb, 04 1979).Google Scholar
[9]Sierpinski, W., Cardinal and ordinal numbers, Second edition revised (PWN-Polish Scientific Publishers, Warszawa, 1965).Google Scholar
[10]White, G., ‘The dual ordinal of a bisimple inverse semigroup’, Semigroup Forum 6 (1973), 295–297.CrossRefGoogle Scholar