Geodesic
On the Jacobson radical of strongly group graded rings
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 3, pp. 575-580.

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For any non-torsion group $G$ with identity $e$, we construct a strongly $G$-graded ring $R$ such that the Jacobson radical $J(R_e)$ is locally nilpotent, but $J(R)$ is not locally nilpotent. This answers a question posed by Puczy{\l}owski.
Classification : 16A03, 16A20, 16N20, 16N40, 16W50
Keywords: strongly graded rings; radicals; local nilpotency 
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     title = {On the {Jacobson} radical of strongly group graded rings},
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Kelarev, A. V. On the Jacobson radical of strongly group graded rings. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 3, pp. 575-580. http://geodesic.mathdoc.fr/item/CMUC_1994__35_3_a15/