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Among the finitely generated modules over a local ring the ones of finite projective dimension are particulary nice. For example, if M= j= 0 is such a module, then the (classical) Auslander-Buchsbaum equality states that depth A—depth M+ pd M, where pd M denotes the projective dimension of M. In [1] Auslander and Bridger has generalized the notion of finite projective dimension to that of finite G-dimension, and they prove a variety of interesting results. For example, they extend the Auslander-Buchsbaum equality to this setup. Furthermore, they prove that a ring A is Gorenstein if and only if every finitely generated A-module M has finite G-dimension. The notion of modules of finite projective dimension has also been generalized in another direction, namely to that of complexes of modules of finite projective dimension, cf. R. Hartshorne [5], and H.-B. Foxby [3] has proved that (most of) the formulas known for modules …