Réseaux sur les anneaux d'entiers algébriques
On Prüfer domains of polynomials.
An analogue of class-number in higher dimensions.
Irreducibility of the iterates of a quadratic polynomial over a field
1. Introduction. Let K be a field of characteristic p ≥ 0 and let f(X) be a polynomial of degree at least two with coefficients in K. We set f₁(X) = f(X) and define for all r ≥ 1. Following R. W. K. Odoni [7], we say that f is stable over K if is irreducible over K for every r ≥ 1. In [6] the same author proved that the polynomial f(X) = X² - X + 1 is stable over ℚ. He wrote in [7] that the proof given there is quite difficult and it would be of interest to have an elementary proof. In the sequel...
Corrections to "Irreducibility of the iterates of a quadratic polynomial over a field" (Acta Arith. 93 (2000), 87-97)
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