Gorenstein dimensions of unbounded complexes under base change
Bull. Korean Math. Soc. 2016 Vol. 53, No. 3, 779-791
https://doi.org/10.4134/BKMS.b150305
Published online May 31, 2016
Dejun Wu
Shanghai Jiao Tong University
Abstract : Transfer of homological properties under base change is a classical field of study. Let $R\rightarrow S$ be a ring homomorphism. The relations of Gorenstein projective (or Gorenstein injective) dimensions of unbounded complexes between $\Ltp{U}{X}$ (or $\RHom{X}{U}$) and $X$ are considered, where $X$ is an $R$-complex and $U$ is an $S$-complex. In addition, some sufficient conditions are given under which the equalities $\Gdimm(\Ltp{U}{X})=\Gdim{X}+\pd{U}$ and $\Gidd(\RHom{X}{U})=\Gdim{X}+\id{U}$ hold.
Keywords : complete projective resolution, Gorenstein projective dimension, local ring homomorphism, depth of complex
MSC numbers : 13D05, 13D07, 13D09
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