Let A be a Noetherian ring of dimension n and P be a projective A module of rank n having trivial determinant. It is proved that if n is even and the image of a generic element g
P
* is a complete intersection, then [P] = [Q
A] in K
0(A) for some projective A module Q of rank n – 1. Further, it is proved that if n is odd, A is Cohen–Macaulay and [P] = [Q
A] in K
0(A) for some projective A module Q of rank n – 1, then P has a unimodular element.
projective module - unimodular element - complete intersection