On serres problem on projective modules

The main purpose of this paper is to prove the following result concerning Serre's problem: Any projective module of rank n over k[X.,''', X ] (where k is an infinite field) is free. We give also simple proofs (based on Serre's theorem that KAkYX., ' ', X ]) = Z) to the following particular case of Bass' theorem: any projective module of rank >n over /t[X., , X ] (k any field) is free, and to Seshadri's theorem: finitely generated projective modules over k\X, Y\ are free.