Abstract: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.
Keywords: strongly graded rings, radicals, local nilpotency
AMS Subject Classification: Primary 16A03; Secondary 16A20