On Ritt's Factorization of Polynomials |
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Authors: | Beardon, A. F. Ng, T. W. |
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Affiliation: | 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 |
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Abstract: | Ritt has shown that any complex polynomial p can be writtenas the composition of polynomials p1,...,pm, where each pj isprime in the sense that it cannot be written as a non-trivialcomposition of polynomials. The factors pj are not unique butthe number m of them is, as is the set of the degrees of thepj. The paper extends Ritt's theory and, in particular, a thirdinvariant of the decomposition is introduced. |
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