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Gorenstein projective dimensions of complexes

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Abstract

We show that over a right coherent left perfect ring R, a complex C of left R-modules is Gorenstein projective if and only if C m is Gorenstein projective in R-Mod for all m ∈ ℤ. Basing on this we show that if R is a right coherent left perfect ring then Gpd(C) = sup{Gpd(C m)|m ∈ ℤ} where Gpd(−) denotes Gorenstein projective dimension.

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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, P. R. China

    Zhong Kui Liu & Chun Xia Zhang

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  1. Zhong Kui Liu
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  2. Chun Xia Zhang
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Correspondence to Zhong Kui Liu.

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Supported by National Natural Science Foundation of China (Grant No. 10961021), TRAPOYT and the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China

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Liu, Z.K., Zhang, C.X. Gorenstein projective dimensions of complexes. Acta. Math. Sin.-English Ser. 27, 1395–1404 (2011). https://doi.org/10.1007/s10114-011-8369-7

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  • DOI: https://doi.org/10.1007/s10114-011-8369-7

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