Existence of unimodular elements in a projective module

(2) Let R be a ring containing Q of even dimension n with height of the Jacobson radical of R≥2. Let P be a projective R[T,T−1]-module of rank n with trivial determinant. Assume that there exists a surjection α:P↠I, where I⊂R[T,T−1] is an ideal of height n such that I is generated by n elements. Then P has a unimodular element (see 3.4).