Geodesic
Homogeneous ideals and Jacobson radical
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 193-195 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{UZERU_2017_51_2_a7,
     author = {N. G. Najaryan},
     title = {Homogeneous ideals and {Jacobson} radical},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {193--195},
     year = {2017},
     volume = {51},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a7/}
}
TY  - JOUR
AU  - N. G. Najaryan
TI  - Homogeneous ideals and Jacobson radical
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2017
SP  - 193
EP  - 195
VL  - 51
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a7/
LA  - en
ID  - UZERU_2017_51_2_a7
ER  - 
%0 Journal Article
%A N. G. Najaryan
%T Homogeneous ideals and Jacobson radical
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2017
%P 193-195
%V 51
%N 2
%U http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a7/
%G en
%F UZERU_2017_51_2_a7
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/

[1] N. Jacobson, Structure of Rings, Amer. Math. Soc. Colloq. Publ., 37, 1956 | MR

[2] N. G. Najaryan, Combinatorial Relations in Algebras with Polynomial Identities, Candidat Dissertation, MSU after M.V. Lomonosov, M., 1985 (in Russian)

[3] S. Nǎstǎsescu, F. Van Oystaeyen, “Jacobson Radials and Maximal Ideals of Normalizing Extension Applied to $z$-Graded Ring”, Common. Algebra, 10:7 (1982), 1839–1847 | MR

[4] S. A. Amitsur, “The $T$-Ideals of the Free Rings”, Jour. Lond. Math. Soc., 30 (1955), 470–475 | DOI | MR | Zbl

[5] V. N. Latyshev, “Algorithmic Recognition of Polynomial Identies”, Mathematical Problems in Cybernetics, 2002, no. 11, 5–15 (in Russian) | MR