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FCP-投射模与某些环(英文)
引用本文:朱占敏,陈建龙.FCP-投射模与某些环(英文)[J].浙江大学学报(理学版),2010,37(2):126-130.
作者姓名:朱占敏  陈建龙
作者单位:1. 嘉兴学院数学系,浙江,嘉兴,314001
2. 东南大学数学系,江苏,南京,210096
基金项目:The NSFC of China (No. 10971024).
摘    要:设R为一个环,如果对每一有限余相关右R-模A,Ext1R(M,A)=0,称一个右R-模M是FCP-投射的.如果有限余生成内射右R-模的有限余生成商模是有限余相关的,则R称为右余凝聚的.如果有限余生成内射右R-模的有限余生成商模是内射的,则R称为右余半遗传的.本文给出了FCP-投射模的一些特征,用FCP-投射模刻画了右V-环和右半遗传环,给出了右V-环为阿丁半单环的一些条件,研究了右余凝聚环上模的FCP-投射维数,还研究了FCP-投射模为投射模的环.

关 键 词:FCP-投射模  V环  余半遗传环  余凝聚环  FCPP环

FCP-projective modules and some rings
ZHU Zhan-min,CHEN Jian-long.FCP-projective modules and some rings[J].Journal of Zhejiang University(Sciences Edition),2010,37(2):126-130.
Authors:ZHU Zhan-min  CHEN Jian-long
Institution:1.Department of Mathematics,Jiaxing University,Jiaxing 314001,Zhejiang Province,China;2.Department of Mathematics,Southeast University,Nanjing 210096,China)
Abstract:Let R be a ring.A module MR is called FCP-projective if Ext_R~1(M,A)=0 for every finitely corelated right R-module A.A ring R is called right co-coherent if every finitely cogenerated factor module of a finitely cogenerated injective right R-module is finitely corelated.A ring R is called right cc-semihereditary if every finitely cogenerated factor module of a finitely cogenerated injective right R-module is injective.Some characterizations of FCP-projective modules are given;right V-rings and right co-semihereditary rings are characteristics by FCP-projective right R modules.Some conditions under which right V-rings are artinian semisimple rings are given.FCP-projective dimensions of modules over right co-coherent rings are investigated.Rings over which every FCP-projective module is projective are studied.
Keywords:FCP-projective module  V-ring  co-semihereditarg ring  co-coherent ring  FCPP-ring
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