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Products of idempotent endomorphisms of an independence algebra of infinite rank

Published online by Cambridge University Press:  24 October 2008

John Fountain  and
Andrew Lewin
John Fountain
Affiliation:
Department of Mathematics, University of York, Heslington, York YO1 5DD
Andrew Lewin
Affiliation:
Department of Mathematics, University of York, Heslington, York YO1 5DD
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Abstract

In 1966, J. M. Howie characterized the self-maps of a set which can be written as a product (under composition) of idempotent self-maps of the same set. In 1967, J. A. Erdos considered the analogous question for linear maps of a finite dimensional vector space and in 1985, Reynolds and Sullivan solved the problem for linear maps of an infinite dimensional vector space. Using the concept of independence algebra, the authors gave a common generalization of the results of Howie and Erdos for the cases of finite sets and finite dimensional vector spaces. In the present paper we introduce strong independence algebras and provide a common generalization of the results of Howie and Reynolds and Sullivan for the cases of infinite sets and infinite dimensional vector spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 2 , September 1993 , pp. 303 - 319
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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