Some New Class of Four-Dimensional Absolute Valued Algebras

Author(s)	Abdelhadi Moutassim
Country	Morocco
Abstract	An absolute valued algebra is a nonzero real algebra that is equipped with a multiplicative norm \|\|ab\|\| = \|\|a\|\| \|\|b\|\|. We prove that if A is a four-dimensional absolute valued algebras containing a nonzero central element a which satisfies one of the following identities: (1) (a^2, a, a) = 0 or (a, a, a^2) = 0 (2) (a^2, a^2, a) = 0 or (a, a^2, a^2) = 0 (3) (a^2, a^2, a^2) = 0, with (a / a^2) ≠ 0 (4) (a^2, a, a^2) = 0. Then A contains a commutative sub-algebra of dimension two. Moreover, A is isomorphic to A_1, A_2, A_3, A_4, B_1 or B_2 in the first two cases and isomorphic to A_1, A_2, A_3, A_4, B_1, B_2, B_3 or B_4, in the last two cases.
Keywords	Absolute valued Algebra, Pre-Hilbert Algebra, Commutative Algebra, Central Element
Field	Mathematics
Published In	Volume 5, Issue 2, March-April 2023
Published On	2023-04-26
Cite This	Some New Class of Four-Dimensional Absolute Valued Algebras - Abdelhadi Moutassim - IJFMR Volume 5, Issue 2, March-April 2023. DOI 10.36948/ijfmr.2023.v05i02.2642
DOI	https://doi.org/10.36948/ijfmr.2023.v05i02.2642
Short DOI	https://doi.org/gr7hgt

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