| ∞-余纯平坦模 |
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| 引用本文： | 熊涛,王芳贵,吴小英.∞-余纯平坦模[J].吉林大学学报(理学版),2017,55(3):519-522. |
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| 作者姓名： | 熊涛 王芳贵 吴小英 |
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| 作者单位： | 1. 西华师范大学 数学与信息学院， 四川 南充 637002； 2. 四川师范大学 数学与软件科学学院, 成都 61006 |
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| 摘 要： | 通过引入∞-余纯平坦模,证明了:R是QF环当且仅当R是左Noether环,且每个有限表现左R-模是∞-余纯平坦模;R是右IF环当且仅当每个左R-模是∞-余纯平坦模;R是左CFH环当且仅当∞-余纯平坦模对子模封闭;左凝聚环R是左半遗传环当且仅当∞-余纯平坦左R-模是平坦的.
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| 关 键 词： | &infin CFH环 半遗传环 IF环 QF环 余纯平坦模 |
| 收稿时间： | 2016-03-23 |
∞ Copure Flat Modules |
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| XIONG Tao,WANG Fanggui,WU Xiaoying.∞ Copure Flat Modules[J].Journal of Jilin University: Sci Ed,2017,55(3):519-522. |
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| Authors: | XIONG Tao WANG Fanggui WU Xiaoying |
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| Institution: | 1. College of Mathematic & Information, China West Normal University, Nanchong 637002, Sichuang Province, China; 2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, China |
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| Abstract: | By introducing the ∞ copure flat modules, we proved that R is a QF ring if and only if R is left Noetherian ring and every finitely presented left R module is ∞ copure flat; R is a right IF ringif and only if every left R module is ∞ copure flat; R is a leftCFH ring if and only if ∞ copure flat modules are closed to their submodules;a left coherent ring R is a semihereditary ring if and only if ∞ copure flat left R modules are flat. |
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| Keywords: | ∞ copure flat module IF ring semihereditary ring CFH ring QF ring |
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