On Absolute Valued Algebras Containing a Central Algebraic Element
Let be an absolute valued algebra containing a nonzero central algebraic element. Then is a pre-Hilbert algebra and is finite dimensional in the following cases:
1) A satisfies (x, x, x)=0.
2) A satisfies (x2, x2 , x2 )=0.
3) A satisfies (x, x2, x)=0.
In these cases is isomorphic to or . It may be conjectured that every absolute valued algebra containing a nonzero central element is pre-Hilbert algebra.