| 内射模的t－平坦性 |
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| 引用本文： | 蒋方明,陈建龙.内射模的t－平坦性[J].数学进展,1996(3). |
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| 作者姓名： | 蒋方明 陈建龙 |
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| 作者单位： | 南京理工大学应用数学系，东南大学数学力学系 |
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| 摘 要： | 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．
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| 关 键 词： | 遗传挠理论 内射模 t－平坦模 |
t-Flatness of Injective Modules |
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| Jiang Fangming.t-Flatness of Injective Modules[J].Advances in Mathematics,1996(3). |
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| Authors: | Jiang Fangming |
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| Abstract: | 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. |
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| Keywords: | hereditary torsion theory injective module t-flat module |
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