Gorenstein Dimensions and Gorenstein Rings

Many of the main results from the theory of homological dimensions over commutative Noetherian rings—developed here in, primarily, Sects. 15.4, 16.3, 16.4, 17.3, and 17.5—have counterparts in the theory of Gorenstein homological dimensions; they are treated in Sects. 19.2–19.4. The first section revisits the Auslander and Bass categories from Chap. 10 and their relation to Gorenstein homological dimensions. The final Sect. 19.5 covers rings of finite Gorenstein global dimension and, more generally, Gorenstein rings.