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Bull. Korean Math. Soc. 2015; 52(1): 137-147

Printed January 31, 2015

https://doi.org/10.4134/BKMS.2015.52.1.137

Copyright © The Korean Mathematical Society.

Balance for relative homology with respect to semidualizing modules

Zhenxing Di, Xiaoxiang Zhang, and Jianlong Chen

Southeast University, Southeast University, Southeast University

Abstract

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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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