Polynomial identities in nil-algebras

Aladova, Elena; Krasilnikov, Alexei

doi:10.1090/S0002-9947-09-04977-0

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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