In this paper we introduce the notion of relative syzygy modules. We then study the extension closure of the category of modules consisting of relative syzygy modules (resp. relative к-torsionfree modules).
There is a variety of nice results about strongly Gorenstein flat modules over coherent rings. These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of these results, and to give hom...There is a variety of nice results about strongly Gorenstein flat modules over coherent rings. These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of these results, and to give homological descriptions of the strongly Gorenstein flat dimension (of modules and rings) over arbitrary associative rings.展开更多
One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A A B = 0, then A B is a summa...One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A A B = 0, then A B is a summand of M. In addition to injective and direct-injective modules, the class of C3-modules includes the semisimple, continuous, indecomposable and regular modules. Indeed, every commutative ring is a C3-ring. In this paper we provide a general and unified treatment of the above mentioned classes of modules in terms of the C3-condition, and establish new characterizations of several well known classes of rings.展开更多
The category consisting of finitely generated modules which are left orthogonal with a cotilting bimodule is shown to be functorially finite. The notion of left orthogonal dimension is introduced , and then a necessar...The category consisting of finitely generated modules which are left orthogonal with a cotilting bimodule is shown to be functorially finite. The notion of left orthogonal dimension is introduced , and then a necessary and sufficient condition of selforthogonal modules having finite injective dimension and a characterization of cotilting modules are given.展开更多
In this paper,we give a relationship between projective generators（resp.,injective cogenerators） in the category of R-modules and the counterparts in the category of complexes of R-modules.As a consequence,we get th...In this paper,we give a relationship between projective generators（resp.,injective cogenerators） in the category of R-modules and the counterparts in the category of complexes of R-modules.As a consequence,we get that complexes of W^--Gorenstein modules are actually W-Gorenstein complexes whenever W is a subcategory of R-modules satisfying W⊥W,where W^- is the subcategory of exact complexes with all cycles in W.We also study when all cycles of a W-Gorenstein complexes are W^--Gorenstein modules.展开更多
In this paper, a characterization of continuous module homomorphisms on random semi-normed modules is first given; then the characterization is further used to show that the Hahn-Banach type of extension theorem is st...In this paper, a characterization of continuous module homomorphisms on random semi-normed modules is first given; then the characterization is further used to show that the Hahn-Banach type of extension theorem is still true for continuous module homomorphisms on random semi-normed modules.展开更多
We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight s...We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenber-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module （and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series）.展开更多
The 2009 swine-origin influenza virus (S-OIV,H1N1 subtype) has developed into a new pandemic influenza as announced by the World Health Organization.In order to uncover clues about the determinants for virulence and p...The 2009 swine-origin influenza virus (S-OIV,H1N1 subtype) has developed into a new pandemic influenza as announced by the World Health Organization.In order to uncover clues about the determinants for virulence and pathogenicity of the virus,we characterized the functional modules of the surface glycoprotein hemagglutinin (HA),the most important protein in molecular epidemiology and pathogenesis of influenza viruses.We analyzed receptor binding sites,basic patch,neutralization antibody epitopes and T cell epitopes in the HA protein of the current S-OIV according to the corresponding functional and structural modules previously characterized in other H1 HA molecules or HA molecules of other subtypes.We compared their differences and similarities systematically.Based on the amino acids defined as the functional and structural modules,the HA protein of 2009 S-OIV should specifically bind to the human 2,6-receptor.The D225G/E mutation in HA,which is found in some isolates,may confer dual binding specificity to the 2,3and 2,6-receptor based on previously reported work.This HA variant contains two basic patches,one of which results in increased basicity,suggesting enhanced membrane fusion function.The 2009 S-OIV HA also has an extra glycosylation site at position 276.Four of the five antibody neutralization epitopes identified in A/RP/8/34(H1N1) were exposed,but the other was hidden by a glycosylation site.The previously identified cytotoxic T cell epitopes in various HA molecules were summarized and their corresponding sequences in 2009 S-OIV HA were defined.These results are critical for understanding the pathogenicity of the virus and host immune response against the virus.展开更多
基金The author was partially supported by the National Natural Science Foundation of China(Grant No.10001017)Scientifc Research Foundation for Returned Overseas Chinese Scholars(State Education Ministry) Nanjing University Talent Development Foundation.
文摘In this paper we introduce the notion of relative syzygy modules. We then study the extension closure of the category of modules consisting of relative syzygy modules (resp. relative к-torsionfree modules).
文摘There is a variety of nice results about strongly Gorenstein flat modules over coherent rings. These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of these results, and to give homological descriptions of the strongly Gorenstein flat dimension (of modules and rings) over arbitrary associative rings.
文摘One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A A B = 0, then A B is a summand of M. In addition to injective and direct-injective modules, the class of C3-modules includes the semisimple, continuous, indecomposable and regular modules. Indeed, every commutative ring is a C3-ring. In this paper we provide a general and unified treatment of the above mentioned classes of modules in terms of the C3-condition, and establish new characterizations of several well known classes of rings.
文摘The category consisting of finitely generated modules which are left orthogonal with a cotilting bimodule is shown to be functorially finite. The notion of left orthogonal dimension is introduced , and then a necessary and sufficient condition of selforthogonal modules having finite injective dimension and a characterization of cotilting modules are given.
基金Supported by National Natural Science Foundation of China(Grant Nos.11301240,11371187 and 11101197)the Young Scholars Science Foundation of Lanzhou Jiaotong University(Grant No.2012020)
文摘In this paper,we give a relationship between projective generators（resp.,injective cogenerators） in the category of R-modules and the counterparts in the category of complexes of R-modules.As a consequence,we get that complexes of W^--Gorenstein modules are actually W-Gorenstein complexes whenever W is a subcategory of R-modules satisfying W⊥W,where W^- is the subcategory of exact complexes with all cycles in W.We also study when all cycles of a W-Gorenstein complexes are W^--Gorenstein modules.
文摘In this paper, a characterization of continuous module homomorphisms on random semi-normed modules is first given; then the characterization is further used to show that the Hahn-Banach type of extension theorem is still true for continuous module homomorphisms on random semi-normed modules.
基金NSF Grants 10471096,10571120 of China"One Hundred Talents Program"from the University of Science and Technology of China
文摘We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenber-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module （and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series）.
基金supported by the National Basic Research Program of China (Grant No. 2010CB534004)an intramural grant from the Chinese Academy of Sciences (Grant No. KSCX2-YW-R-158)
文摘The 2009 swine-origin influenza virus (S-OIV,H1N1 subtype) has developed into a new pandemic influenza as announced by the World Health Organization.In order to uncover clues about the determinants for virulence and pathogenicity of the virus,we characterized the functional modules of the surface glycoprotein hemagglutinin (HA),the most important protein in molecular epidemiology and pathogenesis of influenza viruses.We analyzed receptor binding sites,basic patch,neutralization antibody epitopes and T cell epitopes in the HA protein of the current S-OIV according to the corresponding functional and structural modules previously characterized in other H1 HA molecules or HA molecules of other subtypes.We compared their differences and similarities systematically.Based on the amino acids defined as the functional and structural modules,the HA protein of 2009 S-OIV should specifically bind to the human 2,6-receptor.The D225G/E mutation in HA,which is found in some isolates,may confer dual binding specificity to the 2,3and 2,6-receptor based on previously reported work.This HA variant contains two basic patches,one of which results in increased basicity,suggesting enhanced membrane fusion function.The 2009 S-OIV HA also has an extra glycosylation site at position 276.Four of the five antibody neutralization epitopes identified in A/RP/8/34(H1N1) were exposed,but the other was hidden by a glycosylation site.The previously identified cytotoxic T cell epitopes in various HA molecules were summarized and their corresponding sequences in 2009 S-OIV HA were defined.These results are critical for understanding the pathogenicity of the virus and host immune response against the virus.
