| 交换环上的平坦模是w-模 |
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| 引用本文： | 赵松泉,王芳贵,陈翰林.交换环上的平坦模是w-模[J].四川师范大学学报(自然科学版),2012,35(3):364-366. |
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| 作者姓名： | 赵松泉 王芳贵 陈翰林 |
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| 作者单位： | 1. 西南科技大学理学院,四川绵阳,621010
2. 四川师范大学数学与软件科学学院,四川成都,610066 |
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| 摘 要： | 设R是有单位元的交换环,R-模M称为w-模,是指对任何满足RHomR(J,R)的有限生成理想J,有HomR(R/J,M)=0与Ext1R(R/J,M)=0.证明了平坦模一定是w-模.
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| 关 键 词： | GV-理想 GV-无挠模 平坦模 w-模 |
Fl.t Modules over a Commutative Ring are w-Modules |
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| ZHAO Song-quan
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WANG Fang-gui
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CHEN Han-lin.Fl.t Modules over a Commutative Ring are w-Modules[J].Journal of Sichuan Normal University(Natural Science),2012,35(3):364-366. |
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| Authors: | ZHAO Song-quan WANG Fang-gui CHEN Han-lin |
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| Institution: | 1(1.College of Sciences,Southwest University of Science and Technology,Mianyang 621010,Sichuan; 2.College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan) |
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| Abstract: | Let R be a commutative ring with identity and denote GV(R) the set of GV-ideals of R.An R-module M is called a w-module if HomR(R/J,M)=0 and Ext1R(R/J,M)=0 for all J∈ GV(R).In this article,it is proved that flat modules over a commutative ring are w-modules. |
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| Keywords: | GV-ideal GV-torsion-free module flat module w-module |
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