Bases for projective modules in <f>An(k)</f>

Let <f>An(k)</f> be the Weyl algebra, with <f>k</f> a field of characteristic zero. It is known that every projective finitely generated left module is free or isomorphic to a left ideal. Let <f>M</f> be a left submodule of a free module. In this paper we give an algorithm to compute the projective dimension of <f>M</f>. If <f>M</f> is projective and <f>rank(M)≥2</f> we give a procedure to find a basis. [Copyright &y& Elsevier]