Geodesic
Algebraic Lie algebras of bounded degree
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 5, pp. 209-242.

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The paper discusses the questions of coincidence of the basic nil-radicals on classes of algebraic Lie algebras and proves the local finite-dimensionality of Lie algebras with an algebraic adjoint representation of bounded degree over fields of sufficiently large positive characteristic. 
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A. Yu. Golubkov. Algebraic Lie algebras of bounded degree. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 5, pp. 209-242. http://geodesic.mathdoc.fr/item/FPM_2019_22_5_a20/

[1] Bakhturin Yu. A., Tozhdestva v algebrakh Li, Nauka, M., 1985 | MR

[2] Beidar K. I., Mikhalev A. V., Slinko A. M., “Kriterii pervichnosti nevyrozhdennykh alternativnykh i iordanovykh algebr”, Tr. MMO, 50, 1987, 130–137 | Zbl

[3] Beidar K. I., Pikhtilkov S. A., “O pervichnom radikale spetsialnykh algebr Li”, UMN, 49:1 (1994), 233 | MR | Zbl

[4] Golubkov A. Yu., “Lokalnaya konechnost algebr”, Fundament. i prikl. matem., 19:6 (2014), 25–75

[5] Golubkov A. Yu., “Konstruktsii spetsialnykh radikalov algebr”, Fundament. i prikl. matem., 20:1 (2015), 57–133

[6] Golubkov A. Yu., “Radikal Kostrikina i podobnye emu radikaly algebr Li”, Fundament. i prikl. matem., 21:2 (2016), 157–180

[7] Grishkov A. N., “O lokalnoi nilpotentnosti ideala algebry Li, porozhdennogo elementami 2-go poryadka”, Sib. matem. zhurn., 23:1 (1982), 181–182 | MR | Zbl

[8] Dzhekobson N., Stroenie kolets, Izd. inostr. lit., M., 1961

[9] Dzhekobson H., Algebry Li, Mir, M., 1964

[10] Zhevlakov K. A., Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR

[11] Zhevlakov K. A., Shestakov I. P., “O lokalnoi konechnosti v smysle Shirshova”, Algebra i logika, 12:1 (1973), 41–73 | MR

[12] Zelmanov E. I., “Absolyutnye deliteli nulya i algebraicheskie iordanovy algebry”, Sib. matem. zhurn., 23:6 (1980), 100–116 | MR

[13] Zelmanov E. I., “Algebry Li s algebraicheskim prisoedinennym predstavleniem”, Mat. sb., 121(163):4(8) (1983), 545–561 | MR

[14] Zelmanov E. I., Kostrikin A. I., “Teorema o sendvichevykh algebrakh”, Tr. Matem. in-ta AN SSSR, 183, 1988, 106–111 | MR

[15] Kostrikin A. I., “Koltsa Li, udovletvoryayuschie usloviyu Engelya”, Izv. AN SSSR. Ser. matem., 21 (1957), 515–540 | Zbl

[16] Kostrikin A. I., Vokrug Bernsaida, Nauka, M., 1986 | MR

[17] Kuzmin E. N., “Algebraicheskie mnozhestva v algebrakh Maltseva”, Algebra i logika, 7:2 (1968), 42–47 | MR | Zbl

[18] Lambek I., Koltsa i moduli, Mir, M., 1971 | MR

[19] Lvov I. V., Teorema Brauna o radikale konechno porozhdennoi PI-algebry, Preprint No 63, In-t matem. SO AN SSSR, Novosibirsk, 1984 | Zbl

[20] Maltsev A. I., Algebraicheskie sistemy, Nauka, M., 1970 | MR

[21] Markov V. T., “O razmernosti nekommutativnykh affinnykh algebr”, Izv. AN SSSR. Ser. matem., 37 (1973), 284–288 | Zbl

[22] Parfenov V. A., “O slabo razreshimom radikale algebr Li”, Sib. matem. zhurn., 12:1 (1971), 171–176 | MR | Zbl

[23] Plotkin B. I., “Ob algebraicheskikh mnozhestvakh elementov v gruppakh i algebrakh Li”, Uspekhi matem. nauk, 13:6(84) (1958), 133–138 | MR | Zbl

[24] Razmyslov Yu. P., Tozhdestva algebr i ikh predstavlenii, Nauka, M., 1989 | MR

[25] Amayo R. K., Stewart I. N., Infinite Dimensional Lie Algebras, Noordhoof, Leyden, 1974 | MR | Zbl

[26] Baxter W. E., Martindale W. S. 3-rd., “Central closure of semiprime non-associative rings”, Commun. Algebra, 7:11 (1979), 1103–1132 | DOI | MR | Zbl

[27] Ericson T. S., Martindale W. S., 3-rd, Osborn J. M., “Prime non-associative algebras”, Pacific J. Math., 60:1 (1975), 49–63 | DOI | MR

[28] Fernández López A., García E., Gómez Lozano M., “The Jordan algebras of a Lie algebra”, J. Algebra, 308 (2007), 164–177 | DOI | MR | Zbl

[29] Fernández López A., Golubkov A. Yu., “Lie algebras with an algebraic adjoint representation revisited”, Manuscripta Math., 140:3–4 (2013), 363–376 | MR | Zbl

[30] García E., Gómez Lozano M., “An elemental characterization of strong primeness in Lie algebras”, J. Algebra, 312 (2007), 132–141 | DOI | MR | Zbl

[31] García E., Gómez Lozano M., “A note on a result of Kostrikin”, J. Algebra, 37 (2009), 2405–2409 | MR | Zbl

[32] García E., Gómez Lozano M., “A characterization of the Kostrikin radical of a Lie algebra”, J. Algebra, 346 (2011), 266–283 | DOI | MR | Zbl

[33] Rowen L. H., “Some results on the center of ring with polynomial identity”, Bull. Amer. Math. Soc., 1973, no. 1, 219–223 | DOI | MR | Zbl

[34] Rowen L. H., Polynomial Identities in Ring Theory, Pure Appl. Math., 84, Academic Press, London, 1980 | MR | Zbl

[35] Wisbauer R., Modules and Algebras: Bimodule Structure and Group Actions on Algebras Harlow, Pitman Monogr. Surv. Pure Appl. Math., 81, Longman, 1996 | MR