FCP-投射模与某些环(英文)  

FCP-projective modules and some rings

作　　者：朱占敏[1] 陈建龙[2] 

机构地区：[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

出　　处：《浙江大学学报（理学版）》2010年第2期126-130,共5页Journal of Zhejiang University（Science Edition）

基　　金：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.Let R be a ring.A module MR is called FCP-projective if Ext1R（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 co-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.

关 键 词：FCP-投射模 V环 余半遗传环 余凝聚环 FCPP环 

分 类 号：O153[理学—数学]