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ON RITT'S FACTORIZATION OF POLYNOMIALS

Published online by Cambridge University Press:  30 October 2000

A. F. BEARDON  and
T. W. NG
A. F. BEARDON
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB; afb@dpmms.cam.ac.uk
T. W. NG
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB; ntw@dpmms.cam.ac.uk
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Abstract

Ritt has shown that any complex polynomial p can be written as the composition of polynomials p1,…,pm, where each pj is prime in the sense that it cannot be written as a non-trivial composition of polynomials. The factors pj are not unique but the number m of them is, as is the set of the degrees of the pj. The paper extends Ritt's theory and, in particular, a third invariant of the decomposition is introduced.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 62 , Issue 1 , August 2000 , pp. 127 - 138
Copyright
The London Mathematical Society 2000

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