Vanishing of Euler class groups

In this paper, we prove some theorems about vanishing of Euler class groups. For example, suppose B=A[X,f−1] where A[X] is a polynomial ring, f∈A[X] is a non-zero divisor and dim(B)=dim(A)+1⩾3. Then we prove that the Euler class group E(B,L)=0 for any rank one projective B module L.