A class of Locally Nilpotent Commutative Algebras

Abstract

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

12 pages