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Products of idempotents in certain semigroups of transformations

Published online by Cambridge University Press:  20 January 2009

J. M. Howie
J. M. Howie
Affiliation:
University of St. Andrews
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In an earlier paper (5) a description was given in set-theoretic terms of the semigroup generated by the idempotents of a full transformation semigroup , one of the results being that if X is finite then every element of that is not bijective is expressible as a product of idempotents. In view of this it was natural to ask whether by analogy every singular square matrix is expressibleas a product of idempotent matrices. This is indeed the case, as was shown by J. A. Erdos (2). Magill (6) has considered products of idempotents in thesemigroup of all continuous self-maps of a topological space X, but a comparable characterization of products of idempotents in this case appears to be extremelydifficult, and no solution is available yet.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 3 , June 1971 , pp. 223 - 236
Copyright
Copyright © Edinburgh Mathematical Society 1971

References

REFERENCES

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