Homogeneous ideals and Jacobson radical

In this paper the Jacobson radical of an algebra $F\langle X\rangle/H$ is studied, where $F\langle X\rangle$ is a free associative algebra of countable rank over infinite field $F$ and $ H$ is a homogeneous ideal of the algebra $F\langle X\rangle$. The following theorem is proved: the Jacobson radical of an algebra $F\langle X\rangle$ is a nil ideal.