Abstract
We investigate the structure of commutative non-associative algebras satisfying the identity x(x(xy)) = 0. Recently, Correa and Hentzel proved that every commutative algebra satisfying above identity over a field of characteristic ≠ 2 is solvable. We prove that every commutative finite-dimensional algebra 𝔄 over a field F of characteristic ≠ 2, 3 which satisfies the identity x(x(xy)) = 0 is nilpotent. Furthermore, we obtain new identities and properties for this class of algebras.
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Communicated by I. Shestakov.