Stably free modules over R[X] of rank > dimR are free Mathematics of

Mathematics of Computation 80 (2011) 1093-1098. Ihsen Yengui (1). May 7, 2011. Abstract. We prove that for any finite-dimensional ring R and n ≥ dim R + 2, ...
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Stably free modules over R[X] of rank > dim R are free Mathematics of Computation 80 (2011) 1093-1098. Ihsen Yengui (1) May 7, 2011

Abstract We prove that for any finite-dimensional ring R and n ≥ dim R + 2, the group En (R[X]) acts transitively on Umn (R[X]). In particular, we obtain that for any finite-dimensional ring R, all finitely generated stably free modules over R[X] of rank > dim R are free. This result was only known for noetherian rings. The proof we give is short, simple, and constructive.

MSC 2000 : 13C10, 19A13, 14Q20, 03F65. Key words : Stably free modules, Unimodular vectors, Quillen-Suslin Theorem, Hermite rings, Hermite Ring Conjecture, Constructive Mathematics.

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Departement of Mathematics, Faculty of Sciences of Sfax, 3000 Sfax, TUNISIA, email: [email protected].

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