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
The introduction of w-operation in the class of flat modules has been successful. Let R be a ring. An R-module M is called a w-fiat module if Tor1r（M, N） is GV-torsion for all R-modules N. In this paper, we introduc...The introduction of w-operation in the class of flat modules has been successful. Let R be a ring. An R-module M is called a w-fiat module if Tor1r（M, N） is GV-torsion for all R-modules N. In this paper, we introduce the w-operation in Gorenstein homological algebra. An R-module M is called Ding w-flat if there exists an exact sequence of projective R-modules ... → P1 → P0 → p0 → p1 → ... such that M Im（P0 → p0） and such that the functor HomR （-,F） leaves the sequence exact whenever F is w-flat. Several well- known classes of rings are characterized in terms of Ding w-flat modules. Some examples are given to show that Ding w-flat modules lie strictly between projective modules and Gorenstein projective modules. The Ding w-flat dimension （of modules and rings） and the existence of Ding w-flat precovers are also studied.展开更多
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The introduction of w-operation in the class of flat modules has been successful. Let R be a ring. An R-module M is called a w-fiat module if Tor1r（M, N） is GV-torsion for all R-modules N. In this paper, we introduce the w-operation in Gorenstein homological algebra. An R-module M is called Ding w-flat if there exists an exact sequence of projective R-modules ... → P1 → P0 → p0 → p1 → ... such that M Im（P0 → p0） and such that the functor HomR （-,F） leaves the sequence exact whenever F is w-flat. Several well- known classes of rings are characterized in terms of Ding w-flat modules. Some examples are given to show that Ding w-flat modules lie strictly between projective modules and Gorenstein projective modules. The Ding w-flat dimension （of modules and rings） and the existence of Ding w-flat precovers are also studied.
