HOMOGENEOUS IDEALS AND JACOBSON RADICAL - Najaryan, N.G. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2017)
In this paper the Jacobson radical of an algebra$F\langle X\rangle / H$ is studied, where FhXi is a free associative algebra of countable rank over infinite field $F$ and $H$ is a homogeneous ideal of the algebr$F\langle X\rangle$. The following theorem is proved: the Jacobson radical of an algebra $F\langle X\rangle / H$ is a nil ideal.
Keywords: free algebra, Jacobson radical, T-ideal, homogeneous ideal, nil ideal