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Simple Right-Symmetric (1, 1)-Superalgebras

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Algebra and Logic Aims and scope

It is proved that 2-torsion-free simple right-symmetric superrings having a nontrivial idempotent and satisfying a superidentity (x, y, z) + (−1)z(x+y)(z, x, y) + (−1)x(y+z)(y, z, x) = 0 are associative. As a consequence, every simple finitedimensional (1, 1)-superalgebra with semisimple even part over an algebraically closed field of characteristic 0 is associative.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. P. Pozhidaev

  2. Universidade de São Paulo, São Paulo, Brasil

    I. P. Shestakov

  3. Sobolev Institute of Mathematics, Novosibirsk, Russia

    I. P. Shestakov

Authors
  1. A. P. Pozhidaev
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  2. I. P. Shestakov
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Corresponding author

Correspondence to A. P. Pozhidaev.

Additional information

The study was carried out within the framework of the state assignment to Sobolev Institute of Mathematics SB RAS, project No. 0314-2019-0001.

A. P. Pozhidaev is supported by FAPESP, project No. 2018/05372-7.

I. P. Shestakov is supported by FAPESP (project No. 2018/23690-6) and by CNPq (project No. 304313/2019-0).

Translated from Algebra i Logika, Vol. 60, No. 2, pp. 166-175, March-April, 2021. Russian DOI: 10.33048/alglog.2021.60.204.

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Pozhidaev, A.P., Shestakov, I.P. Simple Right-Symmetric (1, 1)-Superalgebras. Algebra Logic 60, 108–114 (2021). https://doi.org/10.1007/s10469-021-09633-z

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  • DOI: https://doi.org/10.1007/s10469-021-09633-z

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