Abstract Let T be a Wakamatsu tilting module. A module M is called （n, T）-copure injective （resp. （n, T）-copure flat） if εT^1（N, M） = 0 （resp. Г1^T（N, M） = 0） for any module N with T-injective dimension ...Abstract Let T be a Wakamatsu tilting module. A module M is called （n, T）-copure injective （resp. （n, T）-copure flat） if εT^1（N, M） = 0 （resp. Г1^T（N, M） = 0） for any module N with T-injective dimension at most n （see Definition 2.2）. In this paper, it is shown that M is （n, T）-copure injective if and only if M is the kernel of an In（T）-precover f ： A → B with A ∈ ProdT. Also, some results on Prod T-syzygies are presented. For instance, it is shown that every nth Prod T-syzygy of every module, generated by T, is （n, T）-copure injective.展开更多
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 Gorenste...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.展开更多
文摘Abstract Let T be a Wakamatsu tilting module. A module M is called （n, T）-copure injective （resp. （n, T）-copure flat） if εT^1（N, M） = 0 （resp. Г1^T（N, M） = 0） for any module N with T-injective dimension at most n （see Definition 2.2）. In this paper, it is shown that M is （n, T）-copure injective if and only if M is the kernel of an In（T）-precover f ： A → B with A ∈ ProdT. Also, some results on Prod T-syzygies are presented. For instance, it is shown that every nth Prod T-syzygy of every module, generated by T, is （n, T）-copure injective.
基金Project supported by the National Natural Science Foundation of China(No.10971090)
文摘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.
