Let R be a commutative noetherian local ring. In this paper, we study Gorenstein projective, injective and flat modules with respect to a semidualizing R-module C, and we give some connections between C-Gorenstein hom...Let R be a commutative noetherian local ring. In this paper, we study Gorenstein projective, injective and flat modules with respect to a semidualizing R-module C, and we give some connections between C-Gorenstein homological dimensions and the Auslander categories of R.展开更多
In this paper, we shall be concerned with what happens of Gorenstein homological dimensions when certain modifications are made to a ring. The five structural operations addressed later are the formation of excellent ...In this paper, we shall be concerned with what happens of Gorenstein homological dimensions when certain modifications are made to a ring. The five structural operations addressed later are the formation of excellent extensions, localizations, Morita equivalences, polynomial extensions and power series extensions.展开更多
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
基金Supported by the National Natural Science Foundation of China(Grant No.11261050)
文摘Let R be a commutative noetherian local ring. In this paper, we study Gorenstein projective, injective and flat modules with respect to a semidualizing R-module C, and we give some connections between C-Gorenstein homological dimensions and the Auslander categories of R.
基金Supported by the National Natural Science Foundation of China (Grant No. 11001222)
文摘In this paper, we shall be concerned with what happens of Gorenstein homological dimensions when certain modifications are made to a ring. The five structural operations addressed later are the formation of excellent extensions, localizations, Morita equivalences, polynomial extensions and power series extensions.
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.
