Abstract
The class of non-commutative hypercomplex number systems (HNS) of 4-dimension constructed by using of non-commutative procedure of Grassman-Clifford doubling of 2-dimensional systems is investigated in the article. All HNS of this class are constructed, algorithms of performance of operations and methods of algebraic characteristics calculation in them, such as conjugation, normalization, a type of zero dividers are investigated. Formulas of exponential functions representation in these systems are displayed.
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