Projective modules over certain non-commutative polynomial rings

Abstract

Let R be the ring D[X1,...,Xn] : The ring of Polynomial over non-commutative division ring D, and An(k) : The Weyl Algebra over a field k or more generally, An(D) over non-commutative division ring D ,where k and D are of characteristic zero. In this work, we study the structure of the finitely generated projective right R- modules Proj(R),the group K0(R) , and the monoid V (R) of the isomorphism classes of these modules .Of particular interest is the classification of the non-free projective right R-modules up to isomorphism in different methods.