The Euler class groups of polynomial rings and unimodular elements in projective modules

Let A be a Noetherian ring of Krull dimension n containing the field of rationals. Let P be a projective A[T]-module of rank n with trivial determinant such that the A-module P/TP has a free summand of rank one. It is proved that if n is even, then P has a free summand of rank one if it maps onto an ideal I of A[T] of height n which is generated by n elements.