| FCG-投射模和FCGP-环 |
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| 引用本文： | 朱占敏.FCG-投射模和FCGP-环[J].河北师范大学学报(自然科学版),2002,26(1):1-3,17. |
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| 作者姓名： | 朱占敏 |
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| 作者单位： | 湖北民族学院数学系,湖北恩施,445000 |
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| 基金项目： | 湖北省教育厅重点科研资助项目 ( 99A0 19) |
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| 摘 要： | 一个左R－模RA称为FCG－投射模，如果对于任一有限余生成模RM，A是M-投射的。环R称为FCGP－环，如果任一FCG－投射R－模都为投射模。给出了FCG－投射模的等价条件，并用FCG－投射模刻画了左V－环和半单环。讨论了FCGP－环的性质和等价条件，得出了R为半单环当且仅当R为左V－环且为FCGP－环，GCGP－环是Morita不变的。
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| 关 键 词： | FCG－投射模 FCGP－环 V－环 半单环 有限余生成模 等价条件 络合环 |
| 文章编号： | 1000-5854(2002)01-0001-03 |
FCG-projective Modules and FCGP-rings |
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| ZHU Zhan-min.FCG-projective Modules and FCGP-rings[J].Journal of Hebei Normal University,2002,26(1):1-3,17. |
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| Authors: | ZHU Zhan-min |
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| Abstract: | A left R-module RA is called a FCG-projective module in case for each finitely cogenerated module RM,A is M-projective.A ring R is said to be a FCGP-ring if each FCG-projective R-module is projective,some equivalent conditions of FCG-projective modules are given,left V-rings and semisimple rings are characterized by FCG-projective modules,characters and equivalent conditions of FCGP-rings are discussed.It is shown that R is a semisimple ring if and only if R is a left V-ring and a FCGP-ring,FCGP-rings are Morita invariant. |
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| Keywords: | FCGP-projective module FCGP-ring V-rings semisimple rings |
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