On the basis of the introduced notion of a parameter of a hypercomplex number system, we propose a new approach to the construction of hypercomplex number systems of rank two over the field of complex numbers. It is shown that quadruplex (bicomplex) numbers and quaternions can be considered as special cases of the universal system of hypercomplex numbers that correspond to certain values of the indicated parameter. We consider the main algebraic properties of the universal system of hypercomplex numbers and give examples illustrating the applicability of the universal hypercomplex system for certain values of the introduced parameter.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 1, pp. 130–139, January, 2011.
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Klipkov, S.I. On a new approach to the construction of hypercomplex number systems of rank two over the field of complex numbers. Ukr Math J 63, 158–168 (2011). https://doi.org/10.1007/s11253-011-0494-z
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DOI: https://doi.org/10.1007/s11253-011-0494-z