Let R and S be rings and R ω S a semidualizing bimodule. We prove that there exists a Morita equivalence between the class of ∞-ω-cotorsionfree 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 semi-tilting modules (resp. Gorenstein artin algebras). Finally we obtain a dual version of the Auslander-Bridger's approximation theorem. As a consequence, we get some equivalent characterizations of Auslander n-Gorenstein artin algebras.