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Algebra Logika, 2010, Volume 49, Number 3, Pages 388–423 (Mi al446)  

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

Isotopes of prime $(-1,1)$- and Jordan algebras

S. V. Pchelintsev

Finance Academy under the Government of the Russian Federation, Moscow, Russia

Abstract: We deal with adjoint commutator and Jordan algebras of isotopes of prime strictly $(-1,1)$-algebras. It is proved that a system of identities of the form $[x_1,x_2,x_2,x_3,…,x_n]$ for $n=2,…,5$ is discernible on isotopes of prime $(-1,1)$-algebras. Also it is shown that adjoint Jordan algebras for suitable isotopes of prime $(-1,1)$-algebras may possess distinct sets of identities. In particular, isotopes of a prime Jordan monster have different sets of identities in general.

Keywords: right alternative algebra, strictly $(-1,1)$-algebra, Jordan algebra, prime algebra, isotope, homotope, identity, Lie nilpotence.

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English version:
Algebra and Logic, 2010, 49:3, 262–288

Bibliographic databases:

UDC: 512.554
Received: 09.09.2009

Citation: S. V. Pchelintsev, “Isotopes of prime $(-1,1)$- and Jordan algebras”, Algebra Logika, 49:3 (2010), 388–423; Algebra and Logic, 49:3 (2010), 262–288

Citation in format AMSBIB
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\by S.~V.~Pchelintsev
\paper Isotopes of prime $(-1,1)$- and Jordan algebras
\jour Algebra Logika
\yr 2010
\vol 49
\issue 3
\pages 388--423
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\zmath{https://zbmath.org/?q=an:1241.17035}
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\transl
\jour Algebra and Logic
\yr 2010
\vol 49
\issue 3
\pages 262--288
\crossref{https://doi.org/10.1007/s10469-010-9095-4}
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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. S. V. Pchelintsev, “Commutator identities of the homotopes of $(-1,1)$-algebras”, Siberian Math. J., 54:2 (2013), 325–340  mathnet  crossref  mathscinet  isi
    2. S. V. Pchelintsev, “On the Commutator Nilpotency Step of Strictly $(-1,1)$-Algebras”, Math. Notes, 93:5 (2013), 756–762  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. S. V. Pchelintsev, “Degenerate alternative algebras”, Siberian Math. J., 55:2 (2014), 323–335  mathnet  crossref  mathscinet  isi
    4. A. V. Grishin, S. V. Pchelintsev, “On centres of relatively free associative algebras with a Lie nilpotency identity”, Sb. Math., 206:11 (2015), 1610–1627  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. Pchelintsev S.V., Shestakov I.P., “Prime (-1,1) and Jordan Monsters and Superalgebras of Vector Type”, J. Algebra, 423 (2015), 54–86  crossref  mathscinet  zmath  isi  elib  scopus
    6. Falcon O.J., Falcon R.M., Nunez J., “a Computational Algebraic Geometry Approach to Enumerate Malcev Magma Algebras Over Finite Fields”, Math. Meth. Appl. Sci., 39:16 (2016), 4901–4913  crossref  mathscinet  zmath  isi  scopus
    7. S. V. Pchelintsev, “Prime algebras connected with monsters”, Siberian Math. J., 59:2 (2018), 341–356  mathnet  crossref  crossref  isi  elib
    8. Falcon R.M., Falcon O.J., Nunez J., “A Historical Perspective of the Theory of Isotopisms”, Symmetry-Basel, 10:8 (2018), 322  crossref  isi  scopus
  • Алгебра и логика Algebra and Logic
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