Gorenstein Homological Dimensions

The invariants treated in this chapter are refinements of the homological dimensions, sometimes referred to as “classic” or “absolute”, that are treated in Chap. 8. The Gorenstein homological dimensions originate in work of Auslander and Bridger [12, 14]. They were introduced to characterize Iwanaga–Gorenstein rings among commutative Noetherian local rings. Studies of Gorenstein homological dimensions over non-commutative rings started with Enochs and collaborators as consolidated and summarized in [102, Chap. 10]. The approach we take in this chapter builds on thiswork as further developed byAvramov and Foxby [28] and Christensen, Frankild, and Holm [64, 73, 74, 152, 153]. The overarching theme is that the Gorenstein homological dimensions behave and interact like the absolute dimensions from Chap. 8.