Injective Dimension of Weyl Algebras over Affine Coefficient Rings

The concern of this paper is to derive formulas for the injective dimension of the n- th Weyl algebra A. (R) in case k is a field of characteristic zero and R is a commutative affine k-algebra of finite injective dimension. For the case n= 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 case R has finite global dimension.