Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using t...Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.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
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
This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationsh...This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified.展开更多
In this paper, a novel interferometric method with a wide range of sensitivities, called holography quasi projection moire, is proposed. It combines the features of the variated double projection moire method and the ...In this paper, a novel interferometric method with a wide range of sensitivities, called holography quasi projection moire, is proposed. It combines the features of the variated double projection moire method and the holographic interferometry method. This technique is used to study the failure modes of microelectronic packaging modules.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
Let R be a ring, and let （F, C） be a cotorsion theory. In this article, the notion of F-perfect rings is introduced as a nontrial generalization of perfect rings and A-perfect rings. A ring R is said to be right dr-...Let R be a ring, and let （F, C） be a cotorsion theory. In this article, the notion of F-perfect rings is introduced as a nontrial generalization of perfect rings and A-perfect rings. A ring R is said to be right dr-perfect if F is projective relative to R for any F ∈ F. We give some characterizations of F-perfect rings. For example, we show that a ring R is right F-perfect if and only if F-covers of finitely generated modules are projective. Moreover, we define F-perfect modules and investigate some properties of them.展开更多
For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and duali...For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.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Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.
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 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 Postdoctoral Science Foundation of China（2017M611851）, the Jiangsu Planned Projects for Postdoctoral Research Funds（1601151C） and the Provincial Natural Science Foundation of Anhui Province（KJ2017A040）
文摘This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified.
基金The project supported by the National Natural Science Foundation of China
文摘In this paper, a novel interferometric method with a wide range of sensitivities, called holography quasi projection moire, is proposed. It combines the features of the variated double projection moire method and the holographic interferometry method. This technique is used to study the failure modes of microelectronic packaging modules.
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.
文摘Let R be a ring, and let （F, C） be a cotorsion theory. In this article, the notion of F-perfect rings is introduced as a nontrial generalization of perfect rings and A-perfect rings. A ring R is said to be right dr-perfect if F is projective relative to R for any F ∈ F. We give some characterizations of F-perfect rings. For example, we show that a ring R is right F-perfect if and only if F-covers of finitely generated modules are projective. Moreover, we define F-perfect modules and investigate some properties of them.
文摘For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.
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.
