A note on projective modules over polynomial rings (Q1077472)

Let A be a commutative noetherian ring and let P be a finitely generated projective A-module. P is said to be ''cancellative'' if \(P\oplus A\cong Q\oplus A\) implies \(P\cong Q\). H. Bass has asked the following question: Let R be a commutative noetherian ring of dimension d and let A denote the polynomial ring \(R[X_ 1,...,X_ n]\). Is every projective A-module of \(rank\quad \geq d+1\) cancellative? In this paper we prove that every projective R[X,Y]-module of \(rank\quad \geq d+1\) \((d=\dim R)\) is cancellative and thus gives the affirmative answer to the question when \(n=2\).