Balance for relative homology with respect to semidualizing modules

摘要

We derive in the paper the tensor product functor $-otimes_R-$ by using proper $mathcal {G}mathcal {P}_C$-resolutions, where $C$ is a semidualizing module. After giving several cases in which different relative homologies agree, we use the Pontryagin duals of $mathcal {G}_C$-projective modules to establish a balance result for such relative homology over a Cohen-Macaulay ring with a dualizing module $D$.