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On the rank of completely 0-simple semigroups

Published online by Cambridge University Press:  24 October 2008

N. Ruškuc
N. Ruškuc
Affiliation:
Department of Mathematical and Computational Sciences, University of St Andrews, St Andrews, KY16 9SS, Scotland
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Abstract

Connected completely 0-simple semigroups are defined by a number of equivalent conditions, and a formula for the rank of these semigroups is proved. As a consequence an alternative proof of the result from [11] is given. In the case of a Rees matrix semigroup M0 [G, I, Λ, P] the rank is expressed in terms of |I|, |Λ|, G and a certain subgroup of G depending on P. At the end the minimal rank of all semigroups M0[G, I, Λ, P] is found for a given group G. Since every completely simple semigroup is connected, every result has a corollary for these semigroups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 2 , September 1994 , pp. 325 - 338
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

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