The Hermite ring conjecture in dimension one

We prove constructively that for any ring R of Krull dimension ⩽1 and n⩾3, the group En(R[X]) acts transitively on Umn(R[X]). In particular, we obtain that for any ring R with Krull dimension ⩽1, all finitely generated stably free modules over R[X] are free. This settles the long-standing Hermite ring conjecture for rings of Krull dimension ⩽1.