On Absolute Valued Algebras Containing a Central Algebraic Element

https://doi.org/10.32996/jmss.2023.4.2.4
Absolute valued algebra, pre-Hilbert algebra, algebraic element, central element.

Authors

  • Abdelhadi Moutassim
    moutassim-1972@hotmail.fr
    Centre Régional des Métier de l’Education et de la Formation, Casablanca-Settat Annexe Provinciale Settat, Morocco
Vol. 4 No. 2 (2023): Journal of Mathematics and Statistics Studies
Articles
April 20, 2023

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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.