Bulletin of the Korean Mathematical Society (대한수학회보)

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GORENSTEIN PROJECTIVE DIMENSIONS OF COMPLEXES UNDER BASE CHANGE WITH RESPECT TO A SEMIDUALIZING MODULE

  • Zhang, Chunxia (School of Mathematical Sciences Chongqing Normal University)
  • Received : 2020.04.21
  • Accepted : 2020.09.23
  • Published : 2021.03.31
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Abstract

Let R → S be a ring homomorphism. The relations of Gorenstein projective dimension with respect to a semidualizing module of homologically bounded complexes between U ⊗LR 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 ${\mathcal{GP}}_{\tilde{C}}-pd_S(S{\otimes}{L \atop R}X)={\mathcal{GP}}_C-pd_R(X)$ holds. As an application it is shown that the Auslander-Buchsbaum formula holds for GC-projective dimension.

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References

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