In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applicati...In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applications are given.展开更多
In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, poly...In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.展开更多
We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein ...We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.展开更多
Du Xianneng和Chen Zhengxin用Gorenstein内射模刻画了Gorenstein环.作者根据Gorenstein投射模来刻画Gorenstein环,利用推出图,得到了定理3.由该文可以看出n-Gorenstein环与Gorenstein投射模的对应关系.在此基础上,又得到了定理4中的两...Du Xianneng和Chen Zhengxin用Gorenstein内射模刻画了Gorenstein环.作者根据Gorenstein投射模来刻画Gorenstein环,利用推出图,得到了定理3.由该文可以看出n-Gorenstein环与Gorenstein投射模的对应关系.在此基础上,又得到了定理4中的两个结论的等价性,在一定意义上拓展了Gorenstein投射模的有关结论.展开更多
基金Supported by the National Natural Science Foundation of China（11361051） Supported by the Program for New Century Excellent the Talents in University（NCET-13-0957）
文摘In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applications are given.
基金Supported by the NNSF of China(10901129)Supported by the SRFDP(20096203120001)
文摘In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.
基金supported by National Natural Science Foundation of China(Grant Nos.12061060 and 11801141)Scientific and Technological Planning Project of Yunnan Province(Grant No.202305AC160005)Scientific and Technological Innovation Team of Yunnan Province(Grant No.2020CXTD25)。
文摘We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.
