Abstract
This is a study of Ding projective modules relative to a semidualizing module and related topics. Firstly, we study [Formula: see text]-projective dimensions and [Formula: see text]-projective modules under change of rings. Secondly, we establish a new version of the Foxby equivalence with respect to [Formula: see text]-projective modules and [Formula: see text]-injective modules. Thirdly, we characterize Ding projective modules in [Formula: see text] and Ding injective modules in [Formula: see text]. At last, as applications, some new characterizations of perfect rings and quasi-Frobenius rings are given.
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