期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
FCG-projective Modules and FCGP-rings
摘要/Abstract
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,FCGP-环是Morita不变的.
A left R-module RA is called a FCG-projective module in case for each finitely cogenerat-ed moduleRM, 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 leftV-ring and a FCGP-ring, FCGP-rings are Morita invariant.