A note on Ritt's theorem on decomposition of polynomials

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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.
F. Dorey and G. Whaples, Prime and composite polynomials,J. Algebra 28 (1972) 88-101. H.T. EngstrBm, Polynomial substitutions, Amer. J. Math.63 (1941) 249-255. M. Fried, On a conjecture of Schur, Michigan Math. J. 17 (1970) 41-55. H. Levi, Composite polynomials with coefficients in an arbitrary field of characteristic zero, Amer.J. Math. 64 (1942) 389-400. J.F. Ritt, Prime and composite polynomials, Trans. Amer.Math. Sot. 23 (1922) 51-66. A. Schinzel, Selected Topics in Polynomials (Section 4,Ritt’s First Theorem; Section 5, Ritt’s Second Theorem) (University of Michigan Press, Ann Arbor, 1982) 12-39.