Gorenstein Projective Dimensions of Complexes  

作　　者：Zhong Kui LIU Chun Xia ZHANG 

机构地区：[1]Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第7期1395-1404,共10页数学学报（英文版）

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

摘　　要：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.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.

关 键 词：Gorenstein projective complex Gorenstein projective module Gorenstein projective dimension projective preenvelope 

分 类 号：O641.4[理学—物理化学] O484[理学—化学]