On Absolute Valued Algebras with a Central Algebraic Element and Satisfying Some Identities
In , we have proven that if is an absolute valued algebra containing a nonzero central algebraic element, then is a pre-Hilbert algebra. Here we show that is finite dimensional in the following cases:
1) A satisfies (x2, x, x) = 0 or (x, x, x2) = 0,
2) A satisfies (x2, x2, x) = 0 or (x, x2, x2) = 0, .
In these cases A is isomorphic to R, C, H or O.