For a commtative ring R and an injective cogenerator E in the category of R-modules, we characterize QF rings, IF rings and semihereditary rings by using the properties of the dual modules with respect to E.
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 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).
The notions of quasi k-Gorenstein algebras and W^t-approximation representations are introduced. The existence and uniqueness (up to projective equivalences) of W^t-approximation representations over quasi k-Gorenstei...The notions of quasi k-Gorenstein algebras and W^t-approximation representations are introduced. The existence and uniqueness (up to projective equivalences) of W^t-approximation representations over quasi k-Gorenstein algebras are established. Some applications of W^t-approximation representations to homologically finite subcategories are given.展开更多
The structure of rightF-⊥ T-approximations of any finitely generated module over an artin algebra Λ is given, relative to an additive subbifunctorF of Ext Λ 1 (-, -) and anF-cotilting moduleT.
基金Supported by National Natural Science Foundation of China (10001017)Scientific Research Foundation for Returned Overseas Chi
文摘For a commtative ring R and an injective cogenerator E in the category of R-modules, we characterize QF rings, IF rings and semihereditary rings by using the properties of the dual modules with respect to E.
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The notions of quasi k-Gorenstein algebras and W^t-approximation representations are introduced. The existence and uniqueness (up to projective equivalences) of W^t-approximation representations over quasi k-Gorenstein algebras are established. Some applications of W^t-approximation representations to homologically finite subcategories are given.
基金This work was supported by the National Natural Science Foundation of China(Grant No. 10001017) Scientific Research Foundation for Returned Overseas Chinese Scholars by the Ministry of Education Nanjing University Talent Development Foundation.
文摘The structure of rightF-⊥ T-approximations of any finitely generated module over an artin algebra Λ is given, relative to an additive subbifunctorF of Ext Λ 1 (-, -) and anF-cotilting moduleT.
