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

Absolute valued algebra, pre-Hilbert algebra, algebraic element, central element


  • Abdelhadi Moutassim
    Centre Régional des Métier de l’Education et de la Formation, Casablanca-Settat Annexe Provinciale Settat, Morocco
April 20, 2023


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.