The Wedderburn Principal Theorem for Generalized Almost-Jordan Algebras

We study commutative algebras A over fields of characteristic ≠2, 3 which satisfy the identity β{x(y(xx)) − x(x(xy))} + γ{y(x(xx)) − x(x(xy))} = 0. We do not assume power-associativity. We find the Peirce decomposition of these algebras. We prove the existence of a Wedderburn decomposition under some additional conditions.

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