| 左广义弱零插入环的一个问题 |
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| 引用本文： | 尚万振,乔小燕. 左广义弱零插入环的一个问题[J]. 吉林大学学报(理学版), 2021, 59(5): 1141-1143. DOI: 10.13413/j.cnki.jdxblxb.2021006 |
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| 作者姓名： | 尚万振 乔小燕 |
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| 作者单位： | 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 |
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| 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anRb=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,Sn(R)是左GWZI环.
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| 关 键 词： | 半交换环 广义弱(GW)-理想 左GWZI环 |
| 收稿时间： | 2021-01-07 |
A Question on Left Generalized Weak Zero Insertive Rings |
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| SHANG Wanzhen,QIAO Xiaoyan. A Question on Left Generalized Weak Zero Insertive Rings[J]. Journal of Jilin University: Sci Ed, 2021, 59(5): 1141-1143. DOI: 10.13413/j.cnki.jdxblxb.2021006 |
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| Authors: | SHANG Wanzhen QIAO Xiaoyan |
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| Affiliation: | 1. Department of Mathematics and Physics Teaching, Taishan College of Science and Technology, Tai’an 271038, Shandong Province, China; 2. School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, Shandong Province, China
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| Abstract: | 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 anRb=0 for some positive integer n. Secondly, we prove that a ring R is a left GWZI ring if and only if so is Sn(R) for any integer n≥2 by using the method of matrix partition. |
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| Keywords: | semicommutative ring generalized weak (GW)-ideal left GWZI ring |
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