Relative copure modules and Foxby equivalence

Abstract

Let R be a commutative ring and C a semidualizing R-module. For a non-negative integer n, we study a natural generalization of copure injective (flat) modules by introducing the concepts of n-C-copure projective (injective, flat) modules and the most important results about copure injective (flat) modules are generalized. Moreover, it is proven that the n-C-copure projective (injective, flat) module is a generalization of C-Gorenstein projective (injective, flat) module and they are the same when the C-Gorenstein global dimension of R is no more than n. At the end, these classes of modules are used to extend the Foxby equivalence.