Abstract
We describe third power associative multiplications ∗ on noncentral Lie ideals of prime algebras and skew elements of prime algebras with involution provided that x ∗ y − y ∗ x = [ x , y ] for all x , y and the prime algebras in question do not satisfy polynomial identities of low degree. We also obtain necessary and sufficient conditions for these multiplications to be fourth power-associative or flexible.
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