On Absolute Valued Algebras Containing a Central Algebraic Element
April 20, 2023
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.
Moutassim, A. (2023). On Absolute Valued Algebras Containing a Central Algebraic Element. Journal of Mathematics and Statistics Studies, 4(2), 38–42. https://doi.org/10.32996/jmss.2023.4.2.4