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arXiv · 0907.3569

A class of Locally Nilpotent Commutative Algebras

Antonio Behn·Alberto Elduque·Alicia Labra
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Abstract

This paper deals with the variety of commutative nonassociative algebras satisfying the identity $L_x^3+ γL_{x^3} = 0$, $γ\in K$. Correa et al proved that if $γ= 0,1$ then any such finitely generated algebra is nilpotent. Here we generalize this result by proving that if $γ\neq -1$, then any such algebra is locally nilpotent. Our results require characteristic $\neq 2,3$.

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Antonio Behn, Alberto Elduque, Alicia Labra. 2009-07-21. A class of Locally Nilpotent Commutative Algebras. https://arxiv.org/abs/0907.3569

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