关于左连续环的若干性质

Some Properties of Left Continuous Rings

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.