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
In this paper,we give a relationship between projective generators（resp.,injective cogenerators） in the category of R-modules and the counterparts in the category of complexes of R-modules.As a consequence,we get th...In this paper,we give a relationship between projective generators（resp.,injective cogenerators） in the category of R-modules and the counterparts in the category of complexes of R-modules.As a consequence,we get that complexes of W^--Gorenstein modules are actually W-Gorenstein complexes whenever W is a subcategory of R-modules satisfying W⊥W,where W^- is the subcategory of exact complexes with all cycles in W.We also study when all cycles of a W-Gorenstein complexes are W^--Gorenstein modules.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.
基金Supported by National Natural Science Foundation of China(Grant Nos.11301240,11371187 and 11101197)the Young Scholars Science Foundation of Lanzhou Jiaotong University(Grant No.2012020)
文摘In this paper,we give a relationship between projective generators（resp.,injective cogenerators） in the category of R-modules and the counterparts in the category of complexes of R-modules.As a consequence,we get that complexes of W^--Gorenstein modules are actually W-Gorenstein complexes whenever W is a subcategory of R-modules satisfying W⊥W,where W^- is the subcategory of exact complexes with all cycles in W.We also study when all cycles of a W-Gorenstein complexes are W^--Gorenstein modules.
