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

DOI:
https://doi.org/10.1090/S0002-9947-09-04977-0

Published electronically:
June 23, 2009

MathSciNet review:
2529907

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Abstract: We prove that in associative algebras over a field of characteristic the polynomial identity is not Specht. To prove this we construct a non-finitely based system of polynomial identities which contains the identity . We also give an example of a non-Specht polynomial identity of degree in unital associative -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:
https://doi.org/10.1090/S0002-9947-09-04977-0

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