Gorenstein projective dimensions of complexes under base change with respect to a semidualizing module
Bull. Korean Math. Soc. 2021 Vol. 58, No. 2, 497-505 https://doi.org/10.4134/BKMS.b200368 Published online December 29, 2020 Printed March 31, 2021
Chunxia Zhang Chongqing Normal University
Abstract : 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)
