Geodesic
On the A.\,V.~Mikhalev's problem for Lie algebras
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 4, pp. 84-89.

Voir la notice de l'article provenant de la source Math-Net.Ru

Weakened A. V. Mikhalev' sproblem about the prime radical of artinian Lie algebras is solved. 
@article{ISU_2013_13_4_a13,
     author = {E. V. Mescherina and O. A. Pikhtilkova and S. A. Pikhtilkov},
     title = {On the {A.\,V.~Mikhalev's} problem for {Lie} algebras},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {84--89},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2013_13_4_a13/}
}
TY  - JOUR
AU  - E. V. Mescherina
AU  - O. A. Pikhtilkova
AU  - S. A. Pikhtilkov
TI  - On the A.\,V.~Mikhalev's problem for Lie algebras
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2013
SP  - 84
EP  - 89
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2013_13_4_a13/
LA  - ru
ID  - ISU_2013_13_4_a13
ER  - 
%0 Journal Article
%A E. V. Mescherina
%A O. A. Pikhtilkova
%A S. A. Pikhtilkov
%T On the A.\,V.~Mikhalev's problem for Lie algebras
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2013
%P 84-89
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2013_13_4_a13/
%G ru
%F ISU_2013_13_4_a13
E. V. Mescherina; O. A. Pikhtilkova; S. A. Pikhtilkov. On the A.\,V.~Mikhalev's problem for Lie algebras. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 4, pp. 84-89. http://geodesic.mathdoc.fr/item/ISU_2013_13_4_a13/

[1] Benkart G., “On inner ideals and ad-nilpotent elements of Lie algebras”, Trans. of the Amer. Math. Soc., 232 (1977), 61–81 | DOI | MR | Zbl

[2] Mescherina E. V., Pikhtilkov S. A., Pikhtilkova O. A., “About properties of Lie algebras inner ideals”, Algebras, algebraic groups and the theory of invariants, Abstracts of the third international school conference, devoted to the 75 anniversary of E. B. Vinberg (Tolyatti, Russia, on June 25–30, 2012), TGU Publ. house, Tolyatti, 2012, 32–34

[3] Mescherina E. V., Pikhtilkov S. A., Pikhtilkova O. A., “On proper inner ideals of simple Lie algebras”, Scientific notes of the Oryol State University, 2012, no. 6, pt. 2, 156–162

[4] Jacobson N., Lie algebras, Mir, Moscow, 1964, 355 pp. | MR

[5] Beidar K. I., Pikhtilkov S. A., “Prime radical of special Lie algebras”, Fundamentalnaya i prikladnaya mathematika, 6:3 (2000), 643–648 | MR | Zbl

[6] Balaba I. N., Mikhalev A. V., Pikhtilkov S. A., “Prime Radical of Graded $\Omega$-groups”, Journal of Mathematical Sciences, 149:2 (2008), 1146–1156 | DOI | MR | Zbl

[7] Pikhtilkov S. A., “Locally Nilpotent Ideals of Special Lie Algebras”, Comm. in Algebra, 29:10 (2001), 3781–3786 | DOI | MR | Zbl