T_C-Gorenstein Projective,L_C-Gorenstein Injective and H_C-Gorenstein Flat Modules  

作　　者：Zhen ZHANG Xiaosheng ZHU Xiaoguang YAN 

机构地区：[1]Department of Primary education,Zibo Normal College [2]Department of Mathematics,Nanjing University [3]Department of Mathematics and Information Technology,Nanjing Xiaozhuang University

出　　处：《Chinese Annals of Mathematics,Series B》2014年第1期115-124,共10页数学年刊（B辑英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.10971090)

摘　　要：The authors introduce and investigate the Tc-Gorenstein projective, Lc- Gorenstein injective and Hc-Gorenstein flat modules with respect to a semidualizing module C which shares the common properties with the Gorenstein projective, injective and flat modules, respectively. The authors prove that the classes of all the Tc-Gorenstein projective or the Hc-Gorenstein flat modules are exactly those Gorenstein projective or flat modules which are in the Auslander class with respect to C, respectively, and the classes of all the Lc-Gorenstein ＇injective modules are exactly those Gorenstein injective modules which are in the Bass class, so the authors get the relations between the Gorenstein projective, injective or flat modules and the C-Gorenstein projective, injective or flat modules. Moreover, the authors consider the Tc（R）-projective and Lc（R）-injective dimensions and Tc（R）-precovers and Lc（R）-preenvelopes. Fiually, the authors study the Hc-Gorenstein flat modules and extend the Foxby equivalences.

关 键 词：Tc-Gorenstein projective module C-Gorenstein projective module Semidualizing module Foxby equivalence PRECOVER Preenvclope 

分 类 号：O153.3[理学—数学] TP311.13[理学—基础数学]