Affine equivalence and Gorensteinness

Recently, Dwyer and Greenless established a Morita-like equivalence between categories consisting of complete modules and torsion modules. It turns out that these categories contain certain full subcategories which may be viewed as "perturbed" Auslander and Bass classes; Auslander and Bass classes are used in the study of so-called Gorenstein dimensions. This observation allows us to prove that any ideal in a commutative, local, Noetherian ring can detect whether or not the underlying ring is Gorenstein.