The Jacobson-radical conjecture for torsion-free graded rings

Let $R=\bigoplus_{n\in G}R_n$ be a ring graded by a torsion-free group $G$, and let $J(R)$ denote its Jacobson radical. An ideal is graded when it is the direct sum of its homogeneous components. The Jacobson-radical conjecture. The Jacobson radical $J(R)$ of every $G$-graded ring is a graded ideal. The paper presents this as a general problem for possibly noncommutative rings and non-Abelian groups; the supplied text gives no resolution.