Abstract
We prove that for any ring R of Krull dimension not greater than 1 and n > 3, the group E-n (R[X, X-1]) acts transitively on Um(n)(R[X, X-1]). In particular, we obtain that for any ring R with Krull dimension not greater than 1, all finitely generated stably free modules over R[X, X-1] are free. All the obtained results are proved constructively.