Injective dimension of Weyl algebras over affine coefficient rings

The concern of this paper is to derive formulas for the injective dimension of then- th Weyl algebraA _n (R) in casek is a field of characteristic zero andR is a commutative affinek-algebra of finite injective dimension. For the casen=1 we prove a more general result from which the above result follows. Such formulas can be viewed as generalizations of the corresponding results given by J. C. McConnell in the caseR has finite global dimension.Project supported in part by the National Natural Science Foundation for Youth