The generalized idempotent conjecture for torsion-free graded rings

Let $R=\bigoplus\limits_{n\in G}R_n$ be a ring graded by a torsion-free group $G$, where $0$ denotes the identity element of $G$. An idempotent is an element $e$ satisfying $e^2=e$. The generalized idempotent conjecture. Every idempotent of $R$ is contained in the base subring $R_0$. The paper settles the analogous assertion in the commutative case, but the stated noncommutative version is not resolved in the supplied text.