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Mat. Sb., 1995, Volume 186, Number 3, Pages 53–64 (Mi msb21)  

This article is cited in 14 scientific papers (total in 14 papers)

Algebras satisfying Capelli identities

K. A. Zubrilin

M. V. Lomonosov Moscow State University

Abstract: Results on the structure of algebras of any finite signature satisfying Capelli identities over fields and Noetherian commutative associative rings are obtained. It is proved that a finitely generated algebra satisfying Capelli identities of some order has a largest solvable ideal. If, in addition, the algebra is semiprime, then it has only finitely many minimal prime ideals. An estimate is given for the nilpotency class of an ideal that is an obstacle to the representability of a finitely generated algebra satisfying Capelli identities.

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English version:
Sbornik: Mathematics, 1995, 186:3, 359–370

Bibliographic databases:

UDC: 519.4
MSC: Primary 17A30; Secondary 17A60
Received: 01.02.1994

Citation: K. A. Zubrilin, “Algebras satisfying Capelli identities”, Mat. Sb., 186:3 (1995), 53–64; Sb. Math., 186:3 (1995), 359–370

Citation in format AMSBIB
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\paper Algebras satisfying Capelli identities
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\yr 1995
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\pages 53--64
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\transl
\jour Sb. Math.
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\pages 359--370
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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. K. A. Zubrilin, “O klasse nilpotentnosti prepyatstviya dlya predstavimosti algebr, udovletvoryayuschikh tozhdestvam Kapelli”, Fundament. i prikl. matem., 1:2 (1995), 409–430  mathnet  mathscinet  zmath
    2. 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
    3. 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
    4. Zubrilin K.A., “Combinatorial aspects of Capelli identities and structure of algebras”, Formal Power Series and Algebraic Combinatorics, 2000, 785–788  isi
    5. 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
    6. A. Ya. Belov, “The Gel'fand–Kirillov dimension of relatively free prime algebras of arbitrary signature”, Russian Math. Surveys, 58:4 (2003), 777–779  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. A. Ya. Belov, “The Gel'fand–Kirillov dimension of relatively free associative algebras”, Sb. Math., 195:12 (2004), 1703–1726  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. 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
    9. A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Siberian Adv. Math., 17:4 (2007), 227–267  mathnet  crossref  mathscinet  elib
    10. 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
    11. 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
    12. Belov-Kanel A. Giambruno A. Rowen L.H. Vishne U., “Zariski Closed Algebras in Varieties of Universal Algebra”, Algebr. Represent. Theory, 17:6 (2014), 1771–1783  crossref  isi
    13. Belov-Kanel A. Rowen L. Vishne U., “Specht'S Problem For Associative Affine Algebras Over Commutative Noetherian Rings”, Trans. Am. Math. Soc., 367:8 (2015), 5553–5596  crossref  mathscinet  zmath  isi
    14. KanelBelov A. Karasik Y. Rowen L., “Computational Aspects of Polynomial Identities: Vol 1, Kemer'S Theorems, 2Nd Edition”, Computational Aspects of Polynomial Identities: Vol 1, Kemer'S Theorems, 2Nd Edition, Monographs and Research Notes in Mathematics, 16, Crc Press-Taylor & Francis Group, 2016, 1–407  mathscinet  isi
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