左广义弱零插入环的一个问题  

A Question on Left Generalized Weak Zero Insertive Rings

作　　者：尚万振 乔小燕[2] SHANG Wanzhen;QIAO Xiaoyan(Department of Mathematics and Physics Teaching,Taishan College of Science and Technology,Tai’an 271038,Shandong Province,China;School of Mathematics and Information Science,Shandong Institute of Business and Technology,Yantai 264005,Shandong Province,China)

机构地区：[1]泰山科技学院数理教学部,山东泰安271038 [2]山东工商学院数学与信息科学学院,山东烟台264005

出　　处：《吉林大学学报（理学版）》2021年第5期1141-1143,共3页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:61972235).

摘　　要：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.

关 键 词：半交换环 广义弱(GW)-理想 左GWZI环 

分 类 号：O153.3[理学—数学]