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

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  • Abdelhadi Moutassim

    (Centre Régional des Métier de l’Education et de la Formation, Casablanca-Settat Annexe Provinciale Settat, Morocco)

Abstract

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.

Suggested Citation

  • Abdelhadi Moutassim, 2023. "On Absolute Valued Algebras with a Central Algebraic Element and Satisfying Some Identities," Journal of Mathematics and Statistics Studies, Al-Kindi Center for Research and Development., vol. 4(2), pages 49-53, April.
    • Handle: RePEc:alk:jmss00:v:4:y:2023:i:2:id:5130
    DOI: 10.32996/jmss.2023.4.2.6
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