$f$-Projective and $f$-Injective Modules |
Received:April 19, 2006 Revised:July 13, 2007 |
Key Words:
$f$-projective module $f$-injective module finitely presented cyclic module (pre)en-\mbox{velope} (pre)cover.
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Fund Project:the Jiangsu Teachers University of Technology of China (No. Kyy06109). |
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Abstract: |
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. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2008.01.011 |
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