Geodesic
On a common generalization of symmetric rings and quasi duo rings
Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 249-258

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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. Various properties of these rings are established and some results on exchange rings and the regularity of left $\mathrm{SF}$-rings are generalized.
Keywords: symmetric ring, Jacobson radical, $J$-symmetric ring. 
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     author = {T. Subedi and D. Roy},
     title = {On a common generalization of symmetric rings and quasi duo rings},
     journal = {Algebra and discrete mathematics},
     pages = {249--258},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a9/}
}
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T. Subedi; D. Roy. On a common generalization of symmetric rings and quasi duo rings. Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 249-258. http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a9/