Geodesic
Homogeneous ideals and Jacobson radical
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 193-195

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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.
Keywords: free algebra, Jacobson radical, $T$-ideal, homogeneous ideal, nil ideal. 
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     title = {Homogeneous ideals and {Jacobson} radical},
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N. G. Najaryan. Homogeneous ideals and Jacobson radical. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 193-195. http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a7/