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

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