耿玉仙.$f$-投射与$f$-内射模[J].数学研究及应用,2008,28(1):74~80 |
$f$-投射与$f$-内射模 |
$f$-Projective and $f$-Injective Modules |
投稿时间:2006-04-19 修订日期:2007-07-13 |
DOI:10.3770/j.issn:1000-341X.2008.01.011 |
中文关键词: |
英文关键词:$f$-projective module $f$-injective module finitely presented cyclic module (pre)en-\mbox{velope} (pre)cover. |
基金项目:江苏技术师范学院基础及应用基础研究基金 (No. Kyy06109). |
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中文摘要: |
设$R$是一个环.称右$R$-模$M$是$f$-投射的,如果对任意$f$-内射模$N$都有$\Ext^{1}(M,N)=0$.令${\cal F}$-proj (${\cal F}$-inj)表示所有$f$-投射模($f$-内射模)的类.本文证明了(${\cal F}$-proj, ${\cal F}$-inj)是一个完备的挠理论;并用$f$-投射模, $f$-内射模对半遗传环, von Neumann正则环以及凝聚环进行了刻划. |
英文摘要: |
Let $R$ be a ring. A right $R$-module $M$ is called $f$-projective if $\Ext^{1}(M,N)$ $=0$ for any $f$-injective right $R$-module N. We prove that (${\cal F}$-proj, ${\cal F}$-inj) is a complete cotorsion theory, where ${\cal F}$-proj~(${\cal F}$-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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