Homological aspects of the dual Auslander transpose, II

Abstract

Let R and S be rings, and let RωS be a semidualizing bimodule. We prove that there exists a Morita equivalence between the class of ∞-ω-cotorsion-free modules and a subclass of the class of ω-adstatic modules. Also, we establish the relation between the relative homological dimensions of a module M and the corresponding standard homological dimensions of Hom(ω,M). By investigating the properties of the Bass injective dimension of modules (resp., complexes), we get some equivalent characterizations of semitilting modules (resp., Gorenstein Artin algebras). Finally, we obtain a dual version of the Auslander–Bridger approximation theorem. As a consequence, we get some equivalent characterizations of Auslander n-Gorenstein Artin algebras.