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Fundam. Prikl. Mat., 1995, Volume 1, Issue 2, Pages 409–430 (Mi fpm83)  

This article is cited in 8 scientific papers (total in 8 papers)

On class of nilpotency of obstruction to embeddability of algebras satisfying Capelli identities

K. A. Zubrilin

M. V. Lomonosov Moscow State University

Abstract: In a finitely generated algebra $L$ satisfying Capelli identities of order $n+1$ over an arbitrary field there exists a nilpotent ideal $I$ such that the class of nilpotency of the ideal $I$ is not greater than $n$ and the quotient algebra $L/I$ is embeddable. It is shown that this bound of class of nilpotency of obstruction (ideal $I$) in the class of algebras of finite signature cannot be improved.

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Received: 01.02.1995

Citation: K. A. Zubrilin, “On class of nilpotency of obstruction to embeddability of algebras satisfying Capelli identities”, Fundam. Prikl. Mat., 1:2 (1995), 409–430

Citation in format AMSBIB
\Bibitem{Zub95}
\by K.~A.~Zubrilin
\paper On class of nilpotency of obstruction to embeddability of algebras satisfying Capelli identities
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 2
\pages 409--430
\mathnet{http://mi.mathnet.ru/fpm83}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1790973}
\zmath{https://zbmath.org/?q=an:0868.16019}


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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. K. A. Zubrilin, “On the largest nilpotent ideal in algebras satisfying Capelli identities”, Sb. Math., 188:8 (1997), 1203–1211  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. K. A. Zubrilin, “On the Baer ideal in algebras satisfying Capelli identities”, Sb. Math., 189:12 (1998), 1809–1818  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Zubrilin K.A., “Combinatorial aspects of Capelli identities and structure of algebras”, Formal Power Series and Algebraic Combinatorics, 2000, 785–788  crossref  mathscinet  zmath  isi
    4. A. Ya. Belov, “No associative $PI$-algebra coincides with its commutant”, Siberian Math. J., 44:6 (2003), 969–980  mathnet  crossref  mathscinet  zmath  isi  elib
    5. A. Ya. Belov, “The Kurosh problem, height theorem, nilpotency of the radical, and algebraicity identity”, J. Math. Sci., 154:2 (2008), 125–142  mathnet  crossref  mathscinet  zmath  elib  elib
    6. A. Ya. Belov, “Burnside-type problems, theorems on height, and independence”, J. Math. Sci., 156:2 (2009), 219–260  mathnet  crossref  mathscinet  zmath  elib  elib
    7. A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Siberian Adv. Math., 17:4 (2007), 227–267  mathnet  crossref  mathscinet  elib
    8. A. Ya. Belov, “The local finite basis property and local representability of varieties of associative rings”, Izv. Math., 74:1 (2010), 1–126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Фундаментальная и прикладная математика
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