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Idempotents in completely 0-simple semigroups

Published online by Cambridge University Press:  18 May 2009

J. M. Howie
J. M. Howie
Affiliation:
The Mathematical Institute, University of St. Andrews
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The structure theorem for completely 0-simple semigroups established by Rees [5] in 1940 has proved a very powerful tool in the investigation of such semigroups. In this paper the theorem is applied to an investigation of the subsemigroup of a completely 0-simple semigroup generated by its idempotents. Previous work on this problem has been carried out by Kim [4], but the present note offers a more direct approach.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 2 , July 1978 , pp. 109 - 113
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

REFERENCES

1.Benzaken, C. and Mayr, H. C., Notion de demi-bande: demi-bandes de type deux, Semigroup Forum 10 (1975), 115–128.CrossRefGoogle Scholar
2.Clifford, A. H., Semigroups admitting relative inverses, Ann. of Math. 42 (1941), 1037–1049.CrossRefGoogle Scholar
3.Howie, J. M., An introduction to semigroup theory (Academic Press, 1976).Google Scholar
4.Kim, Jin Bai, Idempotent generated Rees matrix semigroups, Kyungpook Math. J. 10 (1970), 7–13.Google Scholar
5.Rees, D., On semi-groups, Proc. Cambridge Philos. Soc. 36 (1940), 387–400.CrossRefGoogle Scholar