On Absolute Valued Algebras with a Central Algebraic Element and Satisfying Some Identities
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.
Moutassim, A. (2023). On Absolute Valued Algebras with a Central Algebraic Element and Satisfying Some Identities. Journal of Mathematics and Statistics Studies, 4(2), 49–53. https://doi.org/10.32996/jmss.2023.4.2.6