The Wedderburn principal theorem for generalized almost-Jordan algebras

Abstract

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. Copyright © Taylor & Francis Group, LLC.