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Idempotent rank in finite full transformation semigroups

Published online by Cambridge University Press:  14 November 2011

John M. Howie  and
Robert B. McFadden
John M. Howie
Affiliation:
Department of Mathematical Sciences, University of St Andrews, St Andrews, Scotland, KY16 9SS, U.K
Robert B. McFadden
Affiliation:
Department of Mathematics, University of Louisville, Louisville, Ky 40292, U.S.A.
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Synopsis

The subsemigroup Singn of singular elements of the full transformation semigroup on a finite set is generated by n(n − l)/2 idempotents of defect one. In this paper we extend this result to the subsemigroup K(n, r) consisting of all elements of rank r or less. We prove that the idempotent rank, defined as the cardinality of a minimal generating set of idempotents, of K(n, r) is S(n, r), the Stirling number of the second kind.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 3-4 , 1990 , pp. 161 - 167
Copyright
Copyright © Royal Society of Edinburgh 1990

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References

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