2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166379We investigate the notion of the C-projective dimension of a module, where C is a semidualizing module. When C=R, this recovers the standard projective dimension. We show that three natural definitions of finite C-projective dimension agree, and investigate the relationship between relative cohomology modules and absolute cohomology modules in this setting. Finally, we prove several results that demonstrate the deep connections between modules of finite projective dimension and modules of finite C-projective dimension. In parallel, we develop the dual theory for injective dimension and C-injective dimension.14 pages, final version, minor correction to last question, to appear in Math. ScandCommutative AlgebraRings and Algebras13D02, 13D05, 13D07, 18G15, 18G20, 18G25text