Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Gorenstein projective dimensions of complexes under base change with respect to a semidualizing module

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)