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Some New Class of Absolute Valued Algebras with Left Unit

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Abstract

Let A be an absolute valued algebra with left unit. We prove that if A contains a nonzero central element, then A is finite dimensional and is isomorphic to \({\mathbb {R}, \mathbb {C}}\) or new classes of four and eight–dimensional absolute valued algebras with left unit. This is more general than those results in [2] and [3].

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References

  1. Albert A.A.: Absolute valued real algebras. Ann. Math. 48, 495–501 (1947)

    Article  MATH  Google Scholar 

  2. Benslimane M., Moutassim A., Rochdi A.: Sur les Algèbres Absoluments Valuées Contenant un Elément Central Non Nul. Adv. appl. Clifford alg. 20(1), 13–21 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. El–Mallah M.L.: Absolute valued algebras satisfying (x 2, x, x) = 0. Arch. Math. 77, 378–382 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. F. Hirzebruch, M. Koecher and R. Remmert, Numbers. Springer–Verlag (1991).

  5. Kaidi A.M., Ramirez M.I., Rodriguez A.: Absolute valued algebraic algebras are finite dimensional. J. Algebra 195, 295–307 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  6. Rodriguez A.: One–sided division absolute–valued algebras. Publ. Math. 36, 925–954 (1992)

    MATH  Google Scholar 

  7. A. Rodriguez, Absolute–valued algebras, and absolute–valuable Banach spaces. Advanced courses of mathematical analysis I, 99–155,World Sci. Publ., Hackensack, NJ, (2004).

  8. Urbanik K., Wright F.B.: Absolute valued algebras. Proc. Amer. Math. Soc. 11, 861–866 (1960)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Département de Mathématiques et Informatiques, Faculté des Sciences, B.P. 2121, Tétouan, Morocco

    M. Benslimane & A. Moutassim

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  1. M. Benslimane
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  2. A. Moutassim
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Correspondence to A. Moutassim.

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Benslimane, M., Moutassim, A. Some New Class of Absolute Valued Algebras with Left Unit. Adv. Appl. Clifford Algebras 21, 31–40 (2011). https://doi.org/10.1007/s00006-010-0246-4

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  • DOI: https://doi.org/10.1007/s00006-010-0246-4

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