Abstract
Let R be a commutative Noetherian ring and let C be a semidualizing R-module. It is proved that , which is a generalization of Holm, Gorenstein homological dimensions. J. Pure Appl Algebra 189(1–3):167–193, Theorem 2.28. Also, it is given a condition to verify certain relation between GC-projectives and GC-flats. Indeed, it is shown that every GC-projective module is GC-flat if and only if for every C-injective module I, the character module is in .
Acknowledgements
The author is very grateful to the referee for several comments that greatly improved the paper.