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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