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On Four-Dimensional Absolute Valued Algebras Containing a Nonzero Central Element


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Authors : Abdelhadi Moutassim

Volume/Issue : Volume 8 - 2023, Issue 3 - March

Google Scholar : https://bit.ly/3TmGbDi

Scribd : https://bit.ly/3ZUjsBb

DOI : https://doi.org/10.5281/zenodo.7745592

Abstract : - An absolute valued algebra is a nonzero real algebra that is equipped with a multiplicative norm ||ab|| = ||a|| ||b||. We classify, by an algebraic method, all fourdimensional absolute valued algebras containing a nonzero central element and commutative sub-algebra of dimension two. Moreover, we give some conditions implying that these new algebras having sub-algebras of dimension two.

Keywords : Absolute Valued Algebra; Pre-Hilbert Algebra; Commutative Algebra; Central Element.

- An absolute valued algebra is a nonzero real algebra that is equipped with a multiplicative norm ||ab|| = ||a|| ||b||. We classify, by an algebraic method, all fourdimensional absolute valued algebras containing a nonzero central element and commutative sub-algebra of dimension two. Moreover, we give some conditions implying that these new algebras having sub-algebras of dimension two.

Keywords : Absolute Valued Algebra; Pre-Hilbert Algebra; Commutative Algebra; Central Element.

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