On a common generalization of symmetric rings and quasi duo rings

• Date: 2020
• Main Authors: Subedi, T., Roy, D.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2020
• Subjects: symmetric ring; Jacobson radical; $J$-symmetric ring; 13C99; 16D80; 16U80
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/493
• Journal Title: Algebra and Discrete Mathematics

Let \(J(R)\) denote the Jacobson radical of a ring \(R\). We call a ring \(R\) as \(J\)-symmetric if for any \(a,b, c\in R, abc=0\) implies \(bac\in J(R)\). It turns out that \(J\)-symmetric rings are a common generalization of left (right) quasi-duo rings and  generalized weakly symmetric rings. Va...