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A note on Ritt's theorem on decomposition of polynomials

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Corrales Rodrigáñez, Carmen (1990) A note on Ritt's theorem on decomposition of polynomials. Journal of Pure and Applied Algebra, 68 (3). pp. 293-296. ISSN 0022-4049

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Official URL: http://www.sciencedirect.com/science/article/pii/002240499090086W


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Abstract

It is known [J. F. Ritt, Trans. Am. Math. Soc. 23, 51-66 (1922; JFM 48.0079.01), H. T. Engstrom, Am. J. Math. 63, 249–255 (1941; Zbl 0025.10403), H.Levi, ibid. 64, 389–400 (1942; Zbl 0063.03512), F. Dorey and G. Whaples, J. Algebra
28, 88-101 (1974; Zbl 0286.12102)] that over fields of characteristic zero, if a polynomial f(x) can be decomposed into two different ways as f = f1 o f2 = g1 o g2, then (up
to linear transformations) either f1, f2, g1 and g2 are all trigonometric polynomials, or f1of2 = g1 o g2 is of the form xm o xr · f(x) = xr · (f(x))m o xm. The result holds
over fields of prime characteristic when the involved field extensions are separable and there are no wildly ramified primes. In this note we give an example of a whole family
of polynomials with degrees non divisible by the characteristic of the field having more
than one decomposition.


Item Type:Article
Uncontrolled Keywords:Ritt’s theorem; Decomposition of polynomials
Subjects:Sciences > Mathematics > Number theory
ID Code:20274
Deposited On:07 Mar 2013 12:10
Last Modified:25 Jun 2018 11:14

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