-projective dimensions, Foxby equivalence and -projective modules.

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