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Mat. Tr., 2007, Volume 10, Number 1, Pages 29–96 (Mi mt29)  

This article is cited in 3 scientific papers (total in 3 papers)

On Rings Asymptotically Close to Associative Rings

A. Ya. Belov

Moscow Center for Continuous Mathematical Education

Abstract: The subject of this work is an extension of A. R. Kemer's results to a rather broad class of rings close to associative rings, over a field of characteristic 0 (in particular, this class includes the varieties generated by finite-dimensional alternative and Jordan rings). We prove the finite-basedness of systems of identities (the Specht property), the representability of finitely-generated relatively free algebras, and the rationality of their Hilbert series. For this purpose, we extend the Razymslov-Zubrilin theory to Kemer polynomials. For a rather broad class of varieties, we prove Shirshov's theorem on height.

Key words: PI-algebra, representable algebra, universal algebra, nonassociative algebra, alternative algebra, Jordan algebra, signature, polynomial identity, Hilbert series, Specht problem.

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English version:
Siberian Advances in Mathematics, 2007, 17:4, 227–267

Bibliographic databases:

UDC: 512.552.4+512.554.32+512.664.2
Received: 17.01.2006

Citation: A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Mat. Tr., 10:1 (2007), 29–96; Siberian Adv. Math., 17:4 (2007), 227–267

Citation in format AMSBIB
\Bibitem{Bel07}
\by A.~Ya.~Belov
\paper On Rings Asymptotically Close to Associative Rings
\jour Mat. Tr.
\yr 2007
\vol 10
\issue 1
\pages 29--96
\mathnet{http://mi.mathnet.ru/mt29}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2485366}
\elib{http://elibrary.ru/item.asp?id=9483454}
\transl
\jour Siberian Adv. Math.
\yr 2007
\vol 17
\issue 4
\pages 227--267
\crossref{https://doi.org/10.3103/S1055134407040013}


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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. A. V. Grishin, L. M. Tsybulya, “On the structure of a relatively free Grassmann algebra”, J. Math. Sci., 171:2 (2010), 149–212  mathnet  crossref  mathscinet  elib
    2. 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
    3. 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  scopus
  • Математические труды Siberian Advances in Mathematics
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