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Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 2, Pages 33–38 (Mi ivm6697)  

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

Nilpotency of $n$-tuple Lie algebras and associative $n$-tuple algebras

N. A. Koreshkov

Chair of Algebra and Mathematical Logic, Kazan State University, Kazan, Russia

Abstract: We obtain conditions for the nilpotency of finite-dimensional $n$-tuple Lie algebras and finite-dimensional associative $n$-tuple algebras. The established conditions are analogous to theorems of Engel and Wedderburn for Lie algebras and associative algebras.

Keywords: $n$-multiple Lie algebra, associative $n$-multiple algebra, nilpotency.

Full text: PDF file (153 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:2, 28–32

Bibliographic databases:

UDC: 512.554
Received: 01.11.2007

Citation: N. A. Koreshkov, “Nilpotency of $n$-tuple Lie algebras and associative $n$-tuple algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 2, 33–38; Russian Math. (Iz. VUZ), 54:2 (2010), 28–32

Citation in format AMSBIB
\Bibitem{Kor10}
\by N.~A.~Koreshkov
\paper Nilpotency of $n$-tuple Lie algebras and associative $n$-tuple algebras
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 2
\pages 33--38
\mathnet{http://mi.mathnet.ru/ivm6697}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2667270}
\zmath{https://zbmath.org/?q=an:05673448}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 2
\pages 28--32
\crossref{https://doi.org/10.3103/S1066369X10020040}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649551827}


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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. N. A. Koreshkov, “Triangulation of $n$-tuple solvable Lie algebras”, Russian Math. (Iz. VUZ), 56:2 (2012), 56–59  mathnet  crossref  mathscinet
    2. N. A. Koreshkov, “Lie sheaves of small dimensions”, Russian Math. (Iz. VUZ), 57:11 (2013), 1–16  mathnet  crossref
    3. N. A. Koreshkov, “Lie and Engel theorems for $n$-tuple Lie algebras”, Siberian Math. J., 54:3 (2013), 472–478  mathnet  crossref  mathscinet  isi
    4. N. A. Koreshkov, “Associative $n$-Tuple Algebras”, Math. Notes, 96:1 (2014), 38–49  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. N. A. Koreshkov, “Simple Lie sheaves of small dimension”, Siberian Math. J., 55:3 (2014), 428–439  mathnet  crossref  mathscinet  isi  elib  elib
    6. N. A. Koreshkov, “Tori in simple Lie pencils”, Russian Math. (Iz. VUZ), 60:6 (2016), 40–44  mathnet  crossref  isi
    7. N. A. Koreshkov, “Symmetrical simple Lie sheaves of rank 1”, Siberian Math. J., 57:3 (2016), 513–518  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    8. N. A. Koreshkov, “Inner derivations of simple Lie pencils of rank $1$”, Russian Math. (Iz. VUZ), 61:4 (2017), 11–17  mathnet  crossref  isi
    9. A. V. Zhuchok, “Free rectangular $n$-tuple semigroups”, Chebyshevskii sb., 20:3 (2019), 261–271  mathnet  crossref
    10. Zhuchok A.V., Koppitz J., “Free Products of N-Tuple Semigroups”, Ukr. Math. J., 70:11 (2019), 1710–1726  crossref  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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