On a new approach to the construction of hypercomplex number systems of rank two over the field of complex numbers
By using the introduced notion of a parameter of hypercomplex numerical system, we propose a new approach to the construction of a hypercomplex numerical systems of rank two over a field of complex numbers. We show that quadroplex (bicomplex) numbers and quaternions can be considered as a special c...
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| Date: | 2011 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2011
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2704 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | By using the introduced notion of a parameter of hypercomplex numerical system, we propose a new approach to the construction of a hypercomplex numerical systems of rank two over a field of complex numbers.
We show that quadroplex (bicomplex) numbers and quaternions can be considered as a special cases of the universal system of hypercomplex numbers that correspond to some values of the mentioned parameter.
We consider principal algebraic characteristics of the universal system of hypercomplex numbers.
We also present examples of possible applications of numbers of universal hypercomplex system to certain values of the introduced parameter. |
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