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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Polynomial identities in nil-algebras
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by Elena V. Aladova and Alexei N. Krasilnikov PDF
Trans. Amer. Math. Soc. 361 (2009), 5629-5646 Request permission

Abstract:

We prove that in associative algebras over a field $F$ of characteristic $p \ge 3$ the polynomial identity $x^{2p}=0$ is not Specht. To prove this we construct a non-finitely based system of polynomial identities which contains the identity $x^{2p}=0$. We also give an example of a non-Specht polynomial identity of degree $2p$ in unital associative $F$-algebras.
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Additional Information
  • Elena V. Aladova
  • Affiliation: Department of Algebra, Moscow Pedagogical State University, 14 Krasnoprudnaya St., Moscow 107140, Russia
  • Alexei N. Krasilnikov
  • Affiliation: Department of Mathematics, University of Brasília, 70910-900, Brasília-DF, Brazil
  • Email: alexei@unb.br
  • Received by editor(s): June 7, 2006
  • Published electronically: June 23, 2009
  • Additional Notes: The first author was partially supported by INTAS
    The second author was partially supported by CNPq/FAPDF/PRONEX-Brazil, CNPq/ PADCT-Brazil, FINATEC-Brazil and RFBR-Russia
  • © Copyright 2009 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 5629-5646
  • MSC (2000): Primary 16R10
  • DOI: https://doi.org/10.1090/S0002-9947-09-04977-0
  • MathSciNet review: 2529907