左广义弱零插入环的一个问题

A Question on Left Generalized Weak Zero Insertive Rings

首先,证明含单位元的结合环R是左广义弱零插入(GWZI)环当且仅当对任意的a,b∈R,ab=0蕴含存在正整数n,使得a^(n)Rb=0;其次,利用矩阵分块方法证明环R是左GWZI环当且仅当对任意的整数n≥2,S_(n)(R)是左GWZI环.

Firstly,we prove that a unital associative ring R is a left generalized weak zero insertive(GWZI)ring if and only if ab=0 implies a^(n)Rb=0 for some positive integer n.Secondly,we prove that a ring R is a left GWZI ring if and only if so is S_(n()R)for any integer n≥2 by using the method of matrix partition.