On Absolute Valued Algebras with a Central Algebraic Element and Satisfying Some Identities

https://doi.org/10.32996/jmss.2023.4.2.6
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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In [8], 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.