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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Polynomial identities in nil-algebras


Authors: Elena V. Aladova and Alexei N. Krasilnikov
Journal: Trans. Amer. Math. Soc. 361 (2009), 5629-5646
MSC (2000): Primary 16R10
Published electronically: June 23, 2009
MathSciNet review: 2529907
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04977-0
PII: S 0002-9947(09)04977-0
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
Article copyright: © Copyright 2009 American Mathematical Society