Abstract
We give a constructive proof of the fact that finitely generated projective modules over a polynomial ring with coefficients in a Prufer domain R with Krull dimension <= 1 are extended from R. In particular, we obtain constructively that finitely generated projective R[X-1,...,X-n]-modules, where R is a Bezout domain with Krull dimension <= 1. are free. Our proof is essentially based on a dynamical method for decreasing the Krull dimension and a constructive rereading of the original proof given by Maroscia and Brewer & Costa. Moreover, we obtain a simple constructive proof of a result due to Lequain and Simis stating that finitely generated modules over R[X-1,...,X-n], n >= 2, are extended from R if and only if this holds for n = 1, where R is an arithmetical ring with finite Krull dimension. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim