Some Remarks on Projective Generators and Injective Cogenerators  

作　　者：Li LIANG Nan Qing DING Gang YANG 

机构地区：[1]School of Mathematics and Physics,Lanzhou Jiaotong University [2]Department of Mathematics,Nanjing University

出　　处：《Acta Mathematica Sinica,English Series》2014年第12期2063-2078,共16页数学学报（英文版）

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)

摘　　要：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.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.

关 键 词：W-Gorenstein modules Gorenstein projective complexes Gorenstein injective complexes projective generators injective cogenerators 

分 类 号：TM31[电气工程—电机]