摘要
本文的目的是讨论左连续环R何时成为QF环,同时给出环R与全矩阵环(R)n之间互为左连续环的一个刻划,主要结果有:(1)设R是左连续环和左弱内射环,对于任意集A,RA是左投射模,则R是QF环;(2)设R是环,R(RR)是一个左CS模,则R是左连续环当且仅当全矩阵环(R)n是左连续环,对每个n≥1。
In this paper the author discussed the situation when left continuous ring becomes a QFring, gave a relation between ring R and full matrix ring (R)n which are left continuous rings.The main results are the following: (1) Let R be a left continuous and left weakly injective ring.If for any set A, RA is a left projective module. Then R is a QF ring. (2) Let R be a ring. If R(RR) is a left CS module. Then R is a left continuous ring if and only if (R)n is a left continuousring.
出处
《浙江师大学报(自然科学版)》
1998年第4期3-6,共4页
Journal of Zhejiang Normal University(Natoral Sciences)
关键词
左连续环
左拟连续环
左CS模
QF环
left Continuous
left Quasi-continuous
left CS Module
QF Ring