RT Journal Article
T1 A note on Ritt's theorem on decomposition of polynomials
A1 Corrales Rodrigáñez, Carmen
AB 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. Algebra28, 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 (upto 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 holdsover 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 familyof polynomials with degrees non divisible by the characteristic of the field having morethan one decomposition.
PB Elsevier Science B.V. (North-Holland)
SN 0022-4049
YR 1990
FD 1990
LK https://hdl.handle.net/20.500.14352/58332
UL https://hdl.handle.net/20.500.14352/58332
LA eng
NO 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.
DS Docta Complutense
RD 3 may 2024