$f$-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.  
Fund Project:the Jiangsu Teachers University of Technology of China (No. Kyy06109).
Author NameAffiliation
GENG Yu-xian 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 $\Ext^{1}(M,N)$ $=0$ 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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