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Sibirsk. Mat. Zh., 2004, Volume 45, Number 2, Pages 427–451 (Mi smj1080)  

This article is cited in 1 scientific paper (total in 1 paper)

Nilpotency of the alternator ideal of a finitely generated binary $(-1,1)$-algebra

S. V. Pchelintsev

Finance Academy under the Government of the Russian Federation

Abstract: We prove nilpotency of the alternator ideal of a finitely generated binary $(-1,1)$-algebra. An algebra is a binary $(-1,1)$-algebra if its every 2-generated subalgebra is an algebra of type $(-1,1)$. While proving the main theorem we obtain various consequences: a prime finitely generated binary $(-1,1)$-algebra is alternative; the Mikheev radical of an arbitrary binary $(-1,1)$-algebra coincides with the locally nilpotent radical; a simple binary $(-1,1)$-algebra is alternative; the radical of a free finitely generated binary $(-1,1)$-algebra is solvable. Moreover, from the main result we derive nilpotency of the radical of a finitely generated binary $(-1,1)$-algebra with an essential identity.

Keywords: associator, binary $(-1,1)$-algebra, nilpotent algebra, prime algebra

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English version:
Siberian Mathematical Journal, 2004, 45:2, 356–375

Bibliographic databases:

UDC: 512.554.5
Received: 03.06.2003

Citation: S. V. Pchelintsev, “Nilpotency of the alternator ideal of a finitely generated binary $(-1,1)$-algebra”, Sibirsk. Mat. Zh., 45:2 (2004), 427–451; Siberian Math. J., 45:2 (2004), 356–375

Citation in format AMSBIB
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\by S.~V.~Pchelintsev
\paper Nilpotency of the alternator ideal of a~finitely generated binary $(-1,1)$-algebra
\jour Sibirsk. Mat. Zh.
\yr 2004
\vol 45
\issue 2
\pages 427--451
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\zmath{https://zbmath.org/?q=an:1059.17022}
\elib{https://elibrary.ru/item.asp?id=5999833}
\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 2
\pages 356--375
\crossref{https://doi.org/10.1023/B:SIMJ.0000021291.69705.6b}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000220959600015}


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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. S. V. Pchelintsev, “Irreducible binary $(-1,1)$-bimodules over simple finite-dimensional algebras”, Siberian Math. J., 47:5 (2006), 934–939  mathnet  crossref  mathscinet  zmath  isi  elib  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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