# Does there exist a projective module over $k[x_1,…,x_n]$ which is not free?

I know that finitely generated projective modules over $k[x_1,...,x_n]$ are free does this result hold for any projective module?

Does there exist a projective module over $k[x_1,...,x_n]$ which is not free?

• I think this is a corollary of the Theorem 4.3 from this paper of Bass. – user26857 Apr 22 '17 at 16:22
• @spohreis Bass' theorem shows that all projective modules over $k[x_1,...,x_n]$ are free. What do you want more then this? – user26857 Oct 11 '17 at 18:40