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 E Z. Basing on this we show that if R is a ...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 E 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.展开更多
基金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
文摘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 E 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.
