Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Mescherina E. V., Pikhtilkov S. A., Pikhtilkova O. A. On the A. V. Mikhalev’s Problem for Lie Algebras. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 84-89. DOI: 10.18500/1816-9791-2013-13-4-84-89

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.11.2013
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Language: 
Russian
Heading: 
Mathematics
UDC: 
512.554.36
DOI: 
10.18500/1816-9791-2013-13-4-84-89

On the A. V. Mikhalev’s Problem for Lie Algebras

Autors: 
Mescherina Elena Vladimirovna, Orenburg State University
Pikhtilkov Sergey Alekseevich, Orenburg State University
Pikhtilkova Ol'ga Aleksandrovna, Orenburg State University
Abstract: 

Weakened A. V. Mikhalev’ sproblem about the prime radical of artinian Lie algebras is solved.

Key words: 
Lie algebra
inner ideal
prime radical
artinian Lie algebra
References: 
  1. Benkart G. On inner ideals and ad-nilpotent elements of Lie algebras. Transaction of the American Mathematical Society, 1977, vol. 232, pp. 61–81.
  2. Mescherina E. V., Pikhtilkov S. A., Pikhtilkova O. A. About properties of Lie algebras inner ideals. Abstracts of the third international school conference «Algebras, algebraic groups and the theory of invariants», devoted to the 75 anniversary of E. B. Vinberg (Tolyatti, Russia, on June 25-30, 2012). Tolyatti, TGU Publ. house, 2012, pp. 32–34 (in Russian).
  3. Mescherina E. V., Pikhtilkov S. A., Pikhtilkova O. A. On proper inner ideals of simple Lie algebras. Uchenye zapiski Orlovskogo gosudarstvennogo universiteta [Scientific notes of the Oryol State University], 2012, no. 6, pt. 2, pp. 156–162 (in Russian).
  4. Jacobson N. Algebry Li [Lie algebras]. Moscow, Mir, 1964, 355 p. (in Russian).
  5. Beidar K. I., Pikhtilkov S. A. Prime radical of special Lie algebras. Fundamentalnaya i prikladnaya mathematika, 2000, vol. 6, no. 3, pp. 643–648 (in Russian).
  6. Balaba I. N., Mikhalev A. V., Pikhtilkov S. A. Prime Radical of Graded ­-groups. Journal of Mathematical Sciences [Fundamentalnaya i prikladnaya mathematika], 2008, vol. 149, no. 2, pp. 1146–1156.
  7. Pikhtilkov S. A. Locally Nilpotent Ideals of Special Lie Algebras. Comm. in Algebra, 2001, vol. 29, no. 10, pp. 3781–3786.
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