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Sets of idempotents that generate the semigroup of singular endomorphisms of a finite-dimensional vector space

Published online by Cambridge University Press:  20 January 2009

R. J. H. Dawlings
R. J. H. Dawlings
Affiliation:
Bayero University, P.M.B. 3011, Kano, Nigeria.
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If M is a mathematical system and End M is the set of singular endomorphisms of M, then End M forms a semigroup under composition of mappings. A number of papers have been written to determine the subsemigroup SM of EndM generated by the idempotents EM of End M for different systems M. The first of these was by J. M. Howie [4]; here the case of M being an unstructured set X was considered. Howie showed that if X is finite, then End X = Sx.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 2 , June 1982 , pp. 133 - 139
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, vol. 1 (Math. Surveys of the American Mathematical Society no. 7, Providence, R.I., 1961).Google Scholar
2.Dawlings, R. J. H., Semigroups of Singular Endomorphisms of Vector Spaces, Ph.D. Thesis (University of St. Andrews, 1980).Google Scholar
3.Erdos, J. A., On products of idempotent matrices, Glasgow Math. J. 8 (1966), 118–122.Google Scholar
4.Howie, J. M., The subsemigroup generated by the idempotents of a full transformation semigroup, J. London Math. Soc. 41 (1966), 707-716.Google Scholar
5.Howie, J. M., An Introduction to Semigroup Theory (Academic Press, 1976).Google Scholar
6.Kim, J. B., Idempotent generated Rees matrix semigroups, Kyungpook Math. J. 10 (1970), 7–13.Google Scholar