Balance for relative homology with respect to semidualizing modules
Bull. Korean Math. Soc. 2015 Vol. 52, No. 1, 137-147
Printed January 31, 2015
Zhenxing Di, Xiaoxiang Zhang, and Jianlong Chen
Southeast University, Southeast University, Southeast University
Abstract : 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 $D$.
Keywords : semidualizing module, Gorenstein dimension, relative homology, balance
MSC numbers : 13D05, 13D07, 18G15, 18G25
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