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Keywords:
strongly graded rings; radicals; local nilpotency
strongly graded rings; radicals; local nilpotency
Summary:
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.
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