Abstract
The aim of this paper is to derive formulas for the global homological dimension of the ring R[θ1,..,θu] of formal linear differential operators over a commutative noetherian ring R with u commuting derivations. Since the case when R has finite global dimension has been completed in [3], the present paper deals mainly with the case when R has infinite global dimension. Formulas are derived which show exactly when R[θ1,.. θu] has finite global dimension, and what the value of that dimension is. Examples are constructed of commutative noetherian domains R such that R is torsion-free as an abelian group, R has infinite global dimension, and R has a derivation such that R[θ] has finite global dimension.
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