On a common generalization of symmetric rings and quasi duo rings. (English) Zbl 1470.16071
A ring \(R\) is called \(J\)-symmetric if \(abc=0\) implies \(bac\in J(R)\) for all \(a,b,c\in R\) where \(J(R)\) is the Jacobson radical of \(R.\) \(J\)-symmetric rings are generalizations of one-sided quasi-duo rings and of weakly symmetric rings.
The authors study various properties of \(J\)-symmetric rings. They show that a \(J\)-symmetric, one-sided SF-ring is strongly regular and that a \(J\)-symmetric, exchange ring is clean.
The authors study various properties of \(J\)-symmetric rings. They show that a \(J\)-symmetric, one-sided SF-ring is strongly regular and that a \(J\)-symmetric, exchange ring is clean.
Reviewer: Lia Vas (Philadelphia)
MSC:
| 16U80 | Generalizations of commutativity (associative rings and algebras) |
| 16N20 | Jacobson radical, quasimultiplication |
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