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Fundam. Prikl. Mat., 2006, Volume 12, Issue 2, Pages 159–174 (Mi fpm939)  

This article is cited in 10 scientific papers (total in 10 papers)

Prime radicals of graded $\Omega$-groups

A. V. Mikhaleva, I. N. Balabab, S. A. Pikhtilkovb

a M. V. Lomonosov Moscow State University
b Tula State Pedagogical University

Abstract: In this paper, we introduce the class of graded $\Omega$-groups, which includes: groups; associative, conformal and vertex algebras; Lie algebras and graded algebras. The graded prime radical of a graded $\Omega$-group is defined, and its elementwise characterization is given. It is shown that the graded prime radical of a graded $\Omega$-groups with a finiteness condition coincides with the lower weakly solvable (in Parfyonov sense) radical.

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English version:
Journal of Mathematical Sciences (New York), 2008, 149:2, 1146–1156

Bibliographic databases:

UDC: 512.552

Citation: A. V. Mikhalev, I. N. Balaba, S. A. Pikhtilkov, “Prime radicals of graded $\Omega$-groups”, Fundam. Prikl. Mat., 12:2 (2006), 159–174; J. Math. Sci., 149:2 (2008), 1146–1156

Citation in format AMSBIB
\Bibitem{MikBalPik06}
\by A.~V.~Mikhalev, I.~N.~Balaba, S.~A.~Pikhtilkov
\paper Prime radicals of graded $\Omega$-groups
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 2
\pages 159--174
\mathnet{http://mi.mathnet.ru/fpm939}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2249699}
\zmath{https://zbmath.org/?q=an:1153.08001}
\elib{http://elibrary.ru/item.asp?id=9307283}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 149
\issue 2
\pages 1146--1156
\crossref{https://doi.org/10.1007/s10958-008-0053-9}
\elib{http://elibrary.ru/item.asp?id=13582339}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38549136753}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. S. A. Pikhtilkov, O. A. Pikhtilkova, “O nekotorykh klassicheskikh radikalakh dlya spetsialnykh algebr Li”, Chebyshevskii sb., 9:1 (2008), 153–157  mathnet  mathscinet
    3. 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  crossref
    4. A. V. Gribov, A. V. Mikhalev, “Prime radical of loops and $\Omega$-loops. I”, J. Math. Sci., 213:2 (2016), 145–157  mathnet  crossref  mathscinet
    5. O. A. Pikhtilkova, S. A. Pikhtilkov, “Local solvability of the prime radical of a weakly artinian Lie algebra”, Siberian Math. J., 57:3 (2016), 549–551  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. A. N. Blagovisnaya, O. A. Pikhtilkova, S. A. Pikhtilkov, “On A. V. Mikhalev problem for weakly Artinian Lie algebras”, J. Math. Sci., 233:5 (2018), 635–639  mathnet  crossref
    7. 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
    8. A. N. Blagovisnaya, O. A. Pikhtilkova, S. A. Pikhtilkov, “On the M.V. Zaicev problem for a Noetherian special Lie algebras”, Russian Math. (Iz. VUZ), 61:5 (2017), 21–25  mathnet  crossref  isi
    9. 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
    10. E. V. Mescherina, O. A. Pikhtilkova, “Razvitie ponyatiya «artinovost» dlya algebr Li”, Chebyshevskii sb., 19:1 (2018), 167–175  mathnet  crossref  elib
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