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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.
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Abstract

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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
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

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