Relative Tilting Modules with Respect to a Semidualizing Module

Let R be a commutative Noetherian ring, and let C be a semidualizing R-module. The notion of C-tilting R-modules is introduced as the relative setting of the notion of tilting R-modules with respect to C. Some properties of tilting and C-tilting modules and the relations between them are mentioned. It is shown that every finitely generated C-tilting R-module is C-projective. Finally, we investigate some kernel subcategories related to C-tilting modules.