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Fundam. Prikl. Mat., 2000, Volume 6, Issue 3, Pages 643–648 (Mi fpm495)  

This article is cited in 16 scientific papers (total in 16 papers)

The prime radical of the special Lie algebras

K. I. Beidara, S. A. Pikhtilkovb

a National Cheng Kung University
b Tula State Pedagogical University

Abstract: The theory of prime radical in generalized special Lie algebras is constructed in the paper. It is shown, that the prime radical is locally solvable. For a field of characteristic zero it is shown that the radical is characteristical and satisfies IDS-property.

Full text: PDF file (314 kB)

Bibliographic databases:
UDC: 512.36+512.34
Received: 01.05.2000

Citation: K. I. Beidar, S. A. Pikhtilkov, “The prime radical of the special Lie algebras”, Fundam. Prikl. Mat., 6:3 (2000), 643–648

Citation in format AMSBIB
\Bibitem{BeiPik00}
\by K.~I.~Beidar, S.~A.~Pikhtilkov
\paper The prime radical of the special Lie algebras
\jour Fundam. Prikl. Mat.
\yr 2000
\vol 6
\issue 3
\pages 643--648
\mathnet{http://mi.mathnet.ru/fpm495}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1801319}
\zmath{https://zbmath.org/?q=an:1001.17004}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Pikhtilkov, SA, “Locally nilpotent ideals of special Lie algebras”, Communications in Algebra, 29:9 (2001), 3781  crossref  mathscinet  zmath  isi
    2. S. A. Pikhtilkov, “On the Prime Radical of $PI$-Representable Groups”, Math. Notes, 72:5 (2002), 682–686  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. A. Pikhtilkov, “O lokalno nilpotentnom radikale spetsialnykh algebr Li”, Fundament. i prikl. matem., 8:3 (2002), 769–782  mathnet  mathscinet  zmath
    4. I. N. Balaba, S. A. Pikhtilkov, “Prime radicals of special Lie superalgebras”, J. Math. Sci., 128:6 (2005), 3365–3371  mathnet  crossref  mathscinet  zmath  elib  elib
    5. S. Pikhtilkov, V. Polyakov, “Artinal special Lie superalgebras”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, no. 1, 116–119  mathnet  mathscinet  zmath
    6. Golubkov, AY, “The prime radical of the special Lie algebras and the elementary Chevalley groups”, Communications in Algebra, 32:5 (2004), 1649  mathscinet  zmath  isi
    7. A. V. Mikhalev, I. N. Balaba, S. A. Pikhtilkov, “Prime radicals of graded $\Omega$-groups”, J. Math. Sci., 149:2 (2008), 1146–1156  mathnet  crossref  mathscinet  zmath  elib  elib
    8. A. Yu. Golubkov, “The radical RN and the weakly solvable radical of linear groups over associative rings”, J. Math. Sci., 154:2 (2008), 143–203  mathnet  crossref  mathscinet  zmath  elib  elib
    9. S. A. Pikhtilkov, O. A. Pikhtilkova, “O lokalno nilpotentnykh radikalakh B. I. Plotkina dlya algebr Li”, Chebyshevskii sb., 8:2 (2007), 83–87  mathnet  mathscinet  zmath
    10. S. A. Pikhtilkov, O. A. Pikhtilkova, “O nekotorykh klassicheskikh radikalakh dlya spetsialnykh algebr Li”, Chebyshevskii sb., 9:1 (2008), 153–157  mathnet  mathscinet
    11. A. A. Kucherov, S. A. Pikhtilkov, O. A. Pikhtilkova, “O gomologicheskom opisanii radikala Dzhekobsona dlya algebr Li”, Chebyshevskii sb., 11:3 (2010), 98–102  mathnet  zmath
    12. A. A. Kucherov, O. A. Pikhtilkova, S. A. Pikhtilkov, “On primitive Lie algebras”, J. Math. Sci., 186:4 (2012), 651–654  mathnet  crossref
    13. E. V. Mescherina, O. A. Pikhtilkova, S. A. Pikhtilkov, “O probleme A. V. Mikhaleva dlya algebr Li”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 13:4(2) (2013), 84–89  mathnet
    14. O. A. Pikhtilkova, S. A. Pikhtilkov, “On special Lie algebras having a faithful module with Krull dimension”, Izv. Math., 81:1 (2017), 91–98  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    15. S. A. Pikhtilkov, O. A. Pikhtilkova, A. N. Blagovisnaya, “O svoistvakh pervichnogo radikala slaboartinovoi algebry Li”, Chebyshevskii sb., 18:1 (2017), 134–142  mathnet  crossref  elib
    16. S. A. Pikhtilkov, O. A. Pikhtilkova, A. A. Gorelik, L. B. Usova, “O gomologicheskom opisanii radikala Dzhekobsona dlya algebr Li i lokalno nilpotentnogo radikala dlya spetsialnykh algebr Li”, Chebyshevskii sb., 18:2 (2017), 195–204  mathnet  crossref  elib
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