JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (6): 1-8.doi: 10.6040/j.issn.1671-9352.0.2022.507

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Quasi-J-clean rings

Yao WANG1(),Jianghuan CHEN1,Yanli REN2,*()   

  1. 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China
    2. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China
  • Received:2022-09-23 Online:2023-06-20 Published:2023-05-23
  • Contact: Yanli REN E-mail:wangyao@nuist.edu.cn;renyanlisx@163.com

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Abstract:

The concept of quasi-J-clean rings is introduced using quasi-idempotent elements. Some examples of quasi-J-clean rings are given and their basic properties are discussed. The following results are proved. (1) If R is a quasi-J-clean ring, then the full matrix ring Mn(R) is a quasi-J-clean ring; (2) A ring R is a UJ-ring if and only if all quasi-clean elements in R are quasi-J-clean elements; (3) If R is a commutative ring, then the necessary and sufficient condition for R to be a quasi-J-clean ring is that R/I=J(R/I)∪U(R/I) if I is an ideal of R contained in J(R) and such that R/I is an indecomposable ring.

Key words: quasi-idempotent element, quasi-J-clean ring, UJ-ring

CLC Number: 

  • O153.3
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