• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.339-356
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• 2014

In this paper, we introduce and discuss the notion of $D_C$-projective modules over commutative rings, where C is a semidualizing module. This extends Gillespie and Ding, Mao's notion of Ding projective modules. The properties of $D_C$-projective dimensions are also given.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.137-147
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• 2015

We derive in the paper the tensor product functor -${\otimes}_R$- by using proper $\mathcal{GP}_C$-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.