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Let R be a regular local ring, and / a regular parameter of R. Quillen asked whether every projective R /-module is free. We settle this question when R is a regular local ring of an affine algebra over a field k. Further, if R has infinite residue field, we show that projective modules over Laurent polynomial extensions of Rf are also free. Introduction. In [Q] Quillen posed the following Question. Let R be a regular local ring and f a regular parameter of R. Are all finitely generateddoi:10.2307/1999568 fatcat:5bvjk2dpdfa6bfxyqcvqxrzp4e