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Products of idempotents in the semigroup of singular endomorphisms of a finite-dimensional vector space

Published online by Cambridge University Press:  14 November 2011

R. J. H. Dawlings
R. J. H. Dawlings
Affiliation:
Bayero University, PMB 3011, Kano, Nigeria
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Synopsis

Let Mn be the semigroup, under composition, of endomorphisms of an n-dimensional vector space. Let E be the set of idempotents of Mn. It has been shown that each singular element of Mn() may be expressed as a composition of elements of E. In this paper the minimum number of idempotents needed in this composition is determined. This is given in terms of n and one parameter dependent on the element. Further, it is shown that En–1⊂<E>, while En=<E>.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 1-2 , 1981 , pp. 123 - 133
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

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