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\({f}\)-Algebra Structure on Hyperbolic Numbers

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Abstract

The algebra of hyperbolic numbers is endowed with a partial order structure. We show that this system of numbers is the only (natural) generalization of real numbers into Archimedean \({f}\)-algebra of dimension two. We establish various properties of hyperbolic numbers related to the \({f}\)-algebra structure. In particular, we generalize fundamental properties of real numbers and give some order interpretations for the two dimensional space-time geometry.

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Authors and Affiliations

  1. Department of Mathematics, Université de Tunis, I.P.E.I.T., 2 Rue Jawaher Lel Nehru, Monfleury, 1008, Tunis, Tunisia

    Hichem Gargoubi

  2. Department of Mathematics, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092, Tunis, Tunisia

    Sayed Kossentini

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  1. Hichem Gargoubi
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  2. Sayed Kossentini
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Gargoubi, H., Kossentini, S. \({f}\)-Algebra Structure on Hyperbolic Numbers. Adv. Appl. Clifford Algebras 26, 1211–1233 (2016). https://doi.org/10.1007/s00006-016-0644-3

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