In this paper,we investigate n-cotilting theory in comodule category.We study n-cotilting comodules and generalize them to ∞-cotilting comodules.We focus on their properties and characterizations.Moreover,we introduc...In this paper,we investigate n-cotilting theory in comodule category.We study n-cotilting comodules and generalize them to ∞-cotilting comodules.We focus on their properties and characterizations.Moreover,we introduce the concept of n-AIR cotilting comodules,and study the correspondence between n-AIR cotilting comodules and n-cotilting comodules.展开更多
Let R be a Noetherian ring. The projectivity and injectivity of modules over R are discussed. The concept of modules is introduced and the descriptions for co-*-modules over R are given. At last, cotilting modules ove...Let R be a Noetherian ring. The projectivity and injectivity of modules over R are discussed. The concept of modules is introduced and the descriptions for co-*-modules over R are given. At last, cotilting modules over R are characterized by means of co-*-modules.展开更多
It is well known that the concept of cotilting modules generalizes injective cogenerators and in turn,the concept of cosilting modules generalizes cotilting modules.In this paper,we further investigate the close conne...It is well known that the concept of cotilting modules generalizes injective cogenerators and in turn,the concept of cosilting modules generalizes cotilting modules.In this paper,we further investigate the close connections among injective cogenerators,cotilting modules and cosilting modules from the viewpoint of morphism categories.Some applications are also given.展开更多
Let A and F be left and right Noetherian rings and ∧ωr a cotilting bimodule. A necessary and sufficient condition for a finitely generated A-module to be ω-k-torsionfree is given and the extension closure of Tω^i ...Let A and F be left and right Noetherian rings and ∧ωr a cotilting bimodule. A necessary and sufficient condition for a finitely generated A-module to be ω-k-torsionfree is given and the extension closure of Tω^i is discussed. As applications, we give some results of ∧ωr related to l.id（ω） ≤ k.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
Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.
文摘In this paper,we investigate n-cotilting theory in comodule category.We study n-cotilting comodules and generalize them to ∞-cotilting comodules.We focus on their properties and characterizations.Moreover,we introduce the concept of n-AIR cotilting comodules,and study the correspondence between n-AIR cotilting comodules and n-cotilting comodules.
文摘Let R be a Noetherian ring. The projectivity and injectivity of modules over R are discussed. The concept of modules is introduced and the descriptions for co-*-modules over R are given. At last, cotilting modules over R are characterized by means of co-*-modules.
基金Supported by NSFC(Grant Nos.12171230,12271249)NSF of Jiangsu Province of China(Grant No.BK20211358)。
文摘It is well known that the concept of cotilting modules generalizes injective cogenerators and in turn,the concept of cosilting modules generalizes cotilting modules.In this paper,we further investigate the close connections among injective cogenerators,cotilting modules and cosilting modules from the viewpoint of morphism categories.Some applications are also given.
文摘Let A and F be left and right Noetherian rings and ∧ωr a cotilting bimodule. A necessary and sufficient condition for a finitely generated A-module to be ω-k-torsionfree is given and the extension closure of Tω^i is discussed. As applications, we give some results of ∧ωr related to l.id（ω） ≤ k.
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. 11026141,11071111)the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. D7080064,Y6100173)
文摘Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.
