Bull. Korean Math. Soc. 2021; 58(2): 497-505
Online first article December 29, 2020 Printed March 31, 2021
https://doi.org/10.4134/BKMS.b200368
Copyright © The Korean Mathematical Society.
Chunxia Zhang
Chongqing Normal University
Let $R\rightarrow S$ be a ring homomorphism. The relations of Gorenstein projective dimension with respect to a semidualizing module of homologically bounded complexes between $U\otimes_{R}^{\mathbf{L}}X$ and $X$ are considered, where $X$ is an $R$-complex and $U$ is an $S$-complex. Some sufficient conditions are given under which the equality $\mathcal{GP}_{\widetilde{C}}\text{-}\mathrm{pd}_{S}(S\otimes^{\mathbf{L}}_{R}X)=\mathcal{GP}_{C}\text{-}\mathrm{pd}_{R}(X)$ holds. As an application it is shown that the Auslander-Buchsbaum formula holds for $G_{C}$-projective dimension.
Keywords: Semidualizing module, $G_{C}$-projective module, $G_{C}$-projective dimension, ring homomorphism, depth of complex
MSC numbers: Primary 13D25, 16E65
Supported by: This work was financially supported by National Natural Science Foundation of China (11871125) and Natural Science Foundation of Chongqing (cstc 2017jcyjAX0298)
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