内射模的t－平坦性

t-Flatness of Injective Modules

设Ｒ为环，ｔ是左Ｒ－模范畴的一个遗传挠理论．文中证明了下述各点等价：（１）每个内射左Ｒ－模是ｔ－平坦的；（２）每个ｔ－有限表现左Ｒ－模的内射包络是ｔ－平坦的；（３）每个ｔ－有限表现左Ｒ－模是自由Ｒ－模的子模；（４）每个ｔ－有限表现左Ｒ－模是自反的且其对偶模是Ｈ－有限生成的．

Let R be a ring with identity and t be the torsion radical relative to an hereditary torsion theory for the category of left R-modules. It is shown that the following statements are equivalent:(1) Every injective left R-module is t-fiat,(2) the injective hull of every t-finitely presented left R-module is t-flat,(3) every t-finitely presented left R-module is a submodule of a free R-module,(4) every t-finitely presented left R-module is reflexive and its dual module is H-FG.