Bases for Projective modules in An(k)

Abstract

Let $A_n(k)$ be the Weyl algebra, with $k$ a field of characteristic zero. It is known that every projective finitely generated left module is free or isomorphic to a left ideal. Let $M$ be a left submodule of a free module. In this paper we give an algorithm to compute the projective dimension of $M$. If $M$ is projective and $\rk(M) \ge 2$ we give a procedure to find a basis.