Journal of Jilin University Science Edition ›› 2021, Vol. 59 ›› Issue (5): 1141-1143.

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A Question on Left Generalized Weak Zero Insertive Rings

SHANG Wanzhen1, QIAO Xiaoyan2   

  1. 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
  • Received:2021-01-07 Online:2021-09-26 Published:2021-09-26

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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.

Key words: semicommutative ring, generalized weak (GW)-ideal, left GWZI ring

CLC Number: 

  • O153.3
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