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| TC-Gorenstein Projective, LC-Gorenstein Injective andHC-Gorenstein Flat Modules? |
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Citation： |
Zhen ZHANG,Xiaosheng ZHU,Xiaoguang YAN.TC-Gorenstein Projective, LC-Gorenstein Injective andHC-Gorenstein Flat Modules?[J].Chinese Annals of Mathematics B,2014,35(1):115~124 |
| Page view： 1888
Net amount： 1796 |
Authors： |
Zhen ZHANG; Xiaosheng ZHU; Xiaoguang YAN; |
Foundation： |
National Natural Science Foundation of China (No. 10971090). |
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| Abstract： |
The authors introduce and investigate the TC-Gorenstein projective, LCGorenstein
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. Finally, the authors study the HC-Gorenstein
flat modules and extend the Foxby equivalences. |
Keywords： |
TC-Gorenstein projective module, C-Gorenstein projective module,Semidualizing module, Foxby equivalence, Precover, Preenvelope |
Classification： |
13D02, 13D05, 13D07, 16D10, 16D40 |
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