f-Projective and f-Injective Modules 被引量：1

f-Projective and f-Injective Modules

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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. 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.

作者 GENG Yu-xian

机构地区 School of Mathematics and Physics

出处《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第1期74-80,共7页 数学研究与评论（英文版）

基金 the Jiangsu Teachers University of Technology of China(No.Kyy06109)

关键词 f-projective module f-injective module finitbly presented cyclic module （pre）en-velope （pre）cover. f-projective module f-injective module finitbly presented cyclic module （pre）en-velope （pre）cover.

分类号 O153 [理学—基础数学]

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Journal of Mathematical Research and Exposition

2008年第1期

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f-Projective and f-Injective Modules 被引量：1

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