Let $$S$$ be a commutative semigroup. Then the Jacobson radical $$J(R)$$ of each semigroup-graded ring $$R=\sum_{s\in S} R_ s$$ satisfies the formula $$J(R)=\sum_{s\in S}(J(R)\cap R_ s)$$ if and only if $$S$$ is embeddable in a torsion-free abelian group.