Let and be rings, and let be a semidualizing bimodule. We prove that there exists a Morita equivalence between the class of --cotorsion-free modules and a subclass of the class of -adstatic modules. Also, we establish the relation between the relative homological dimensions of a module and the corresponding standard homological dimensions of . 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 -Gorenstein Artin algebras.
"Homological aspects of the dual Auslander transpose, II." Kyoto J. Math. 57 (1) 17 - 53, April 2017. https://doi.org/10.1215/21562261-3759504