Geodesic
Residual finiteness and the Noetherian property of finitely generated Lie algebras
Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 495-504 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A description of locally Noetherian varieties of Lie algebras over a field of characteristic zero is obtained. Also described are the locally residually finite subvarieties of special, locally solvable, and some other varieties of Lie algebras over an infinite field of positive characteristic. Sufficient conditions for the residual finiteness and Noetherian property of finitely generated Lie algebras are found. Bibliography: 13 titles. 
@article{SM_1989_64_2_a13,
     author = {M. V. Zaicev},
     title = {Residual finiteness and the {Noetherian} property of finitely generated {Lie~algebras}},
     journal = {Sbornik. Mathematics},
     pages = {495--504},
     year = {1989},
     volume = {64},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_64_2_a13/}
}
TY  - JOUR
AU  - M. V. Zaicev
TI  - Residual finiteness and the Noetherian property of finitely generated Lie algebras
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 495
EP  - 504
VL  - 64
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1989_64_2_a13/
LA  - en
ID  - SM_1989_64_2_a13
ER  - 
%0 Journal Article
%A M. V. Zaicev
%T Residual finiteness and the Noetherian property of finitely generated Lie algebras
%J Sbornik. Mathematics
%D 1989
%P 495-504
%V 64
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1989_64_2_a13/
%G en
%F SM_1989_64_2_a13
M. V. Zaicev. Residual finiteness and the Noetherian property of finitely generated Lie algebras. Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 495-504. http://geodesic.mathdoc.fr/item/SM_1989_64_2_a13/

[1] Olshanskii A. Yu., “Mnogoobraziya finitno approksimiruemykh grupp”, Izv. AN SSSR. Ser. matem., 33 (1969), 915–927

[2] Ananin A. Z., “Lokalno finitno approksimiruemye i lokalno predstavimye mnogoobraziya algebr”, Algebra i logika, 16:1 (1977), 3–23 | MR

[3] Zaitsev M. V., “Lokalno finitno approksimiruemye mnogoobraziya algebr Li”, Matem. zametki, 44:3 (1988), 352–361 | MR | Zbl

[4] Bakhturin Yu. A., “Ob approksimatsii algebr Li”, Matem. zametki., 12:6 (1972), 713–716 | Zbl

[5] Latyshev V. N., “Obobschenie teoremy Gilberta o konechnosti bazisov”, Sib. matem. zhurn., 7:6 (1966), 1422–1424 | Zbl

[6] Lvov I. V., “Uslovie maksimalnosti v algebrakh s tozhdestvennymi sootnosheniyami”, Algebra i logika, 8:4 (1969), 449–459 | MR

[7] Volichenko I. B., O mnogoobraziyakh tsentralno-metabelevykh algebr Li, Preprint IM AN BSSR No 16 (96), IM AN BSSR, Minsk, 1980

[8] Mischenko S. P., Struktura i tozhdestva nekotorykh razreshimykh mnogoobrazii algebr Li, Dis. $\dots$ kand. fiz.-matem. nauk, MGU, M., 1982

[9] Kostrikin A. I., “O probleme Bernsaida”, Izv. AN SSSR. Ser. matem., 23 (1959), 3–34 | MR

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

[11] Bakhturin Yu. A., Tozhdestva v algebrakh Li, Nauka, M., 1986 | MR

[12] Zelmanov E. I., “Ob engelevykh algebrakh Li”, DAN SSSR, 292:2 (1987), 265–268 | MR

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