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RISS 인기검색어
- 검색키워드
- 저자 : Zenghui Gao (검색결과 9 건)
- 무료
- 기관 내 무료
- 유료
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Gorenstein weak injective modules with respect to a semidualizing bimodule
Zenghui Gao,Xin Ma,Tiwei Zhao 대한수학회 2018 대한수학회지 Vol.55 No.6
In this paper, we introduce the notion of $C$-Gorenstein weak injective modules with respect to a semidualizing bimodule $_SC_R$, where $R$ and $S$ are arbitrary associative rings. We show that an iteration of the procedure used to define $G_C$-weak injective modules yields exactly the $G_C$-weak injective modules, and then give the Foxby equivalence in this setting analogous to that of $C$-Gorenstein injective modules over commutative Noetherian rings. Finally, some applications are given, including weak co-Auslander-Buchweitz context, model structure and dual pair induced by $G_C$-weak injective modules.
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On GI-flat modules and dimensions
Zenghui Gao 대한수학회 2013 대한수학회지 Vol.50 No.1
Let R be a ring. A right R-module M is called GI-flat ifTorR1 (M,G) = 0 for every Gorenstein injective left R-module G. It isshown that GI-flat modules lie strictly between flat modules and copureflat modules. Suppose R is an n-FC ring, we prove that a finitely pre-sented right R-module M is GI-flat if and only if M is a cokernel of aGorenstein flat preenvelope K→F of a right R-module K with F flat. Then we study GI-flat dimensions of modules and rings. Various resultsin [6] are developed, some new characterizations of von Neumann regularrings are given.
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ON GORENSTEIN COTORSION DIMENSION OVER GF-CLOSED RINGS
Gao, Zenghui Korean Mathematical Society 2014 대한수학회보 Vol.51 No.1
In this article, we introduce and study the Gorenstein cotorsion dimension of modules and rings. It is shown that this dimension has nice properties when the ring in question is left GF-closed. The relations between the Gorenstein cotorsion dimension and other homological dimensions are discussed. Finally, we give some new characterizations of weak Gorenstein global dimension of coherent rings in terms of Gorenstein cotorsion modules.
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On Gorenstein cotorsion dimension over GF-closed rings
Zenghui Gao 대한수학회 2014 대한수학회보 Vol.51 No.1
In this article, we introduce and study the Gorenstein cotorsion dimension of modules and rings. It is shown that this dimension has nice properties when the ring in question is left GF-closed. The relations between the Gorenstein cotorsion dimension and other homological dimensions are discussed. Finally, we give some new characterizations of weak Gorenstein global dimension of coherent rings in terms of Gorenstein cotorsion modules.
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ON GI-FLAT MODULES AND DIMENSIONS
Gao, Zenghui Korean Mathematical Society 2013 대한수학회지 Vol.50 No.1
Let R be a ring. A right R-module M is called GI-flat if $Tor^R_1(M,G)=0$ for every Gorenstein injective left R-module G. It is shown that GI-flat modules lie strictly between flat modules and copure flat modules. Suppose R is an $n$-FC ring, we prove that a finitely presented right R-module M is GI-flat if and only if M is a cokernel of a Gorenstein flat preenvelope K ${\rightarrow}$ F of a right R-module K with F flat. Then we study GI-flat dimensions of modules and rings. Various results in [6] are developed, some new characterizations of von Neumann regular rings are given.
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FOXBY EQUIVALENCE RELATIVE TO C-WEAK INJECTIVE AND C-WEAK FLAT MODULES
Zenghui Gao,Tiwei Zhao 대한수학회 2017 대한수학회지 Vol.54 No.5
Let $S$ and $R$ be rings and $_SC_R$ a (faithfully) semidualizing bimodule. We introduce and study $C$-weak flat and $C$-weak injective modules as a generalization of $C$-flat and $C$-injective modules (\cite{HW07}) respectively, and use them to provide additional information concerning the important Foxby equivalence between the subclasses of the Auslander class $\mathcal{A}_C(R)$ and that of the Bass class $\mathcal{B}_C(S)$. Then we study the stability of Auslander and Bass classes, which enables us to give some alternative characterizations of the modules in $\mathcal{A}_C(R)$ and $\mathcal{B}_C(S)$. Finally we consider an open question which is closely relative to the main results (\cite{EJL05}), and discuss the relationship between the Bass class $\mathcal{B}_C(S)$ and the class of Gorenstein injective modules.
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FOXBY EQUIVALENCE RELATIVE TO C-WEAK INJECTIVE AND C-WEAK FLAT MODULES
Gao, Zenghui,Zhao, Tiwei Korean Mathematical Society 2017 대한수학회지 Vol.54 No.5
Let S and R be rings and $_SC_R$ a (faithfully) semidualizing bimodule. We introduce and study C-weak flat and C-weak injective modules as a generalization of C-flat and C-injective modules ([21]) respectively, and use them to provide additional information concerning the important Foxby equivalence between the subclasses of the Auslander class ${\mathcal{A}}_C$ (R) and that of the Bass class ${\mathcal{B}}_C$ (S). Then we study the stability of Auslander and Bass classes, which enables us to give some alternative characterizations of the modules in ${\mathcal{A}}_C$ (R) and ${\mathcal{B}}_C$ (S). Finally we consider an open question which is closely relative to the main results ([11]), and discuss the relationship between the Bass class ${\mathcal{B}}_C$(S) and the class of Gorenstein injective modules.
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GORENSTEIN WEAK INJECTIVE MODULES WITH RESPECT TO A SEMIDUALIZING BIMODULE
Gao, Zenghui,Ma, Xin,Zhao, Tiwei Korean Mathematical Society 2018 대한수학회지 Vol.55 No.6
In this paper, we introduce the notion of C-Gorenstein weak injective modules with respect to a semidualizing bimodule $_SC_R$, where R and S are arbitrary associative rings. We show that an iteration of the procedure used to define $G_C$-weak injective modules yields exactly the $G_C$-weak injective modules, and then give the Foxby equivalence in this setting analogous to that of C-Gorenstein injective modules over commutative Noetherian rings. Finally, some applications are given, including weak co-Auslander-Buchweitz context, model structure and dual pair induced by $G_C$-weak injective modules.
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Intrusion Detection System based on Hidden Conditional Random Fields
Jun Luo,Zenghui Gao 보안공학연구지원센터 2015 International Journal of Security and Its Applicat Vol.9 No.9
Intrusion detection is an important way to ensure the security of computers and networks. In this paper, a new intrusion detection system (IDS) is proposed based on Hidden Conditional Random Fields (HCRFs). In order to optimize the performance of HCRFs, we bring forward the Two-stage Feature Selection method, which contains Manual Feature Selection method and Backward Feature Elimination Wrapper (BFEW) method. The BFEW is a feature selection method which is introduced based on wrapper approach. Experimental results on KDD99 dataset show that the proposed IDS not only has a great advantage in detection efficiency but also has a higher accuracy when compared with other well-known methods.
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