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Journal of the London Mathematical Society 2000 62(1):127-138; doi:10.1112/S0024610700001046
© 2000 by London Mathematical Society
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© The London Mathematical Society

On Ritt's Factorization of Polynomials

A. F. Beardon and T. W. Ng

Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge Wilberforce Road, Cambridge CB3 0WB, afb{at}dpmms.cam.ac.uk
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge Wilberforce Road, Cambridge CB3 0WB, ntw{at}dpmms.cam.ac.uk

Received 10 February 1999. Revision received 18 August 1999.

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.


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