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Products of two idempotent transformations over arbitrary sets and vector spaces

Published online by Cambridge University Press:  17 April 2009

Rachel Thomas
Rachel Thomas
Affiliation:
Department of MathematicsThe University of Western AustraliaNedlands WA 6907Australia
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Abstract

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In this paper we consider the characterisation of those elements of a transformation semigroup S which are a product of two proper idempotents. We give a characterisation where S is the endomorphism monoid of a strong independence algebra A, and apply this to the cases where A is an arbitrary set and where A is an arbitrary vector space. The results emphasise the analogy between the idempotent generated subsemigroups of the full transformation semigroup of a set and of the semigroup of linear transformations from a vector space to itself.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 59 - 71
Copyright
Copyright © Australian Mathematical Society 1998

References

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