Let R be an associative ring with identity,and Y be a class of right R-modules,which contains all injective right R-modules.In this paper,we introduce the definition of Y-Gorenstein cotorsion modules,which is a genera...Let R be an associative ring with identity,and Y be a class of right R-modules,which contains all injective right R-modules.In this paper,we introduce the definition of Y-Gorenstein cotorsion modules,which is a generalization of cotorsion and Gorenstein cotorsion modules.We discuss the relationship between Gorenstein cotorsion,weakly Gorenstein cotorsion and Y-Gorenstein cotorsion modules.We investigate properties and characterizations of Y-Gorenstein cotorsion modules.展开更多
This article is concerned with the strongly Gorenstein flat dimensions of modules and rings.We show this dimension has nice properties when the ring is coherent,and extend the well-known Hilbert＇s syzygy theorem to t...This article is concerned with the strongly Gorenstein flat dimensions of modules and rings.We show this dimension has nice properties when the ring is coherent,and extend the well-known Hilbert＇s syzygy theorem to the strongly Gorenstein flat dimensions of rings.Also,we investigate the strongly Gorenstein flat dimensions of direct products of rings and（almost）excellent extensions of rings.展开更多
基金Supported by the 2020 Scienti c Research Projects in Universities of Gansu Province(Grant No.2020A-277).
文摘Let R be an associative ring with identity,and Y be a class of right R-modules,which contains all injective right R-modules.In this paper,we introduce the definition of Y-Gorenstein cotorsion modules,which is a generalization of cotorsion and Gorenstein cotorsion modules.We discuss the relationship between Gorenstein cotorsion,weakly Gorenstein cotorsion and Y-Gorenstein cotorsion modules.We investigate properties and characterizations of Y-Gorenstein cotorsion modules.
基金Supported by the National Natural Science Foundation of China (Grant No.10961021)
文摘This article is concerned with the strongly Gorenstein flat dimensions of modules and rings.We show this dimension has nice properties when the ring is coherent,and extend the well-known Hilbert＇s syzygy theorem to the strongly Gorenstein flat dimensions of rings.Also,we investigate the strongly Gorenstein flat dimensions of direct products of rings and（almost）excellent extensions of rings.
