| $f$-投射与$f$-内射模 |
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| 引用本文： | 耿玉仙.$f$-投射与$f$-内射模[J].数学研究及应用,2008,28(1):74-80. |
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| 作者姓名： | 耿玉仙 |
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| 作者单位： | School of Mathematics and Physics, Jiangsu Teachers University of Technology, Jiangsu 213001, China |
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| 基金项目： | the Jiangsu Teachers University of Technology of China （No. Kyy06109）. |
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| 摘 要： | Let R be a ring. A fight R-module M is called f-projective if Ext^1 （M, N） = 0 for any f-injective right R-module N. We prove that （F-proj,F-inj） is a complete cotorsion theory, where （F-proj （F-inj） denotes the class of all f-projective （f-injective） right R-modules. Semihereditary rings, von Neumann regular rings and coherent rings are characterized in terms of f-projective modules and f-injective modules.
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| 关 键 词： | f-projective module f-injective module finitely presented cyclic module (pre)envelope (pre)cover 内射模 Neumann regular rings coherent rings characterized modules Semihereditary class complete theory prove right |
| 收稿时间： | 2006-04-19 |
| 修稿时间： | 2007-07-13 |
$f$-Projective and $f$-Injective Modules |
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| GENG Yu-xian.$f$-Projective and $f$-Injective Modules[J].Journal of Mathematical Research with Applications,2008,28(1):74-80. |
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| Authors: | GENG Yu-xian |
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| Institution: | School of Mathematics and Physics,Jiangsu Teachers University of Technology,Jiangsu 213001,China |
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| Abstract: | Let R be a ring.A right R-module M is called f-projective if Ext1(M,N) = 0for any f-injective right R-module N.We prove that (F-proj,F-inj) is a complete cotorsion theory,where F-proj (F-inj) denotes the class of all f-projective (f-injective) right R-modules.Semihereditary rings,von Neumann regular rings and coherent rings are characterized in terms of f-projective modules and f-injective modules. |
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| Keywords: | $f$-projective module $f$-injective module finitely presented cyclic module (pre)en-\mbox{velope} (pre)cover |
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