Abstract
The main properties of bicomplex and hyperbolic numbers are considered, in particular, the three conjugations on them generate the corresponding moduli of a bicomplex number which are not real valued: two of them are complex valued and one is hyperbolic valued. The notion of a positive hyperbolic number allows to introduce a partial order on the set of hyperbolic numbers which has far-reaching consequences in the theory of normed bicomplex modules.
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Alpay, D., Luna-Elizarrarás, M.E., Shapiro, M., Struppa, D.C. (2014). Bicomplex and Hyperbolic Numbers. In: Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-05110-9_1
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DOI: https://doi.org/10.1007/978-3-319-05110-9_1
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Online ISBN: 978-3-319-05110-9
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