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.