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\(f\)-algebra structure on hyperbolic numbers. (English) Zbl 1403.06028

Summary: 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.

MSC:

06F25 Ordered rings, algebras, modules
51N25 Analytic geometry with other transformation groups
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