Quasi-Central Semicommutative Rings
Received:June 27, 2022  Revised:October 05, 2022
Key Words: central semicommutative rings   quasi-central semicommutative rings   duo rings  
Fund Project:Supported by the National Nature Science Foundation of China (Grant No.61972235).
Author NameAffiliation
Yingying WANG School of Mathematics and Information Science, Shandong Institute of Business and Technology, Shandong 264005, P. R. China 
Xiaoyan QIAO School of Mathematics and Information Science, Shandong Institute of Business and Technology, Shandong 264005, P. R. China 
Weixing CHEN School of Mathematics and Information Science, Shandong Institute of Business and Technology, Shandong 264005, P. R. China 
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Abstract:
      A ring $R$ is said to be quasi-central semicommutative (simply, a QCS ring) if $ab=0$ implies $aRb\subseteq Q(R)$ for $a,b\in R$, where $Q(R)$ is the quasi-center of $R$. It is proved that if $R$ is a QCS ring, then the set of nilpotent elements of $R$ coincides with its Wedderburn radical, and that the upper triangular matrix ring $R=T_n(S)$ for any $n\geq 2$ is a QCS ring if and only if $n=2$ and $S$ is a duo ring, while $T_{2k+2}^k(R)$ is a QCS ring when $R$ is a reduced duo ring.
Citation:
DOI:10.3770/j.issn:2095-2651.2023.04.005
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