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Completely zero-simple semigroups generated by nilpotent elements

Published online by Cambridge University Press:  18 May 2009

C. H. Houghton  and
R. P. Sullivan
C. H. Houghton
Affiliation:
Department of Pure Mathematics, University College, Cardiff
R. P. Sullivan
Affiliation:
Department of Mathematics, University of Western Australia
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For a completely 0-simple semigroup, Howie [2] has investigated the subsemigroup generated by the idempotents. Here we determine those elements of such a semigroup which are generated by the set of nilpotent elements and hence we derive a condition for a completely 0-simple semigroup to be nilpotent generated. This condition is purely combinatorial, in terms of the structure of the graph associated with the semigroup, and it includes the case of a non-regular Rees matrix semigroup.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 2 , July 1984 , pp. 163 - 165
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

1.Houghton, C. H., Completely 0-simple semigroups and their associated graphs and groups, Semigroup Forum 14 (1977), 41–67.CrossRefGoogle Scholar
2.Howie, J. M., Idempotents in completely 0-simple semigroups, Glasgow Math. J. 19 (1978), 109–113.CrossRefGoogle Scholar