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Bilgin, Merve; Ersoy, Soley

Algebraic properties of bihyperbolic numbers. (English) Zbl 1442.30049

Adv. Appl. Clifford Algebr. 30, No. 1, Paper No. 13, 17 p. (2020).
Summary: In this paper, we study the four-dimensional real algebra of bihyperbolic numbers. Under consideration of the spectral representation of the bihyperbolic numbers, we give a partial order of bihyperbolic numbers which allows us to obtain some relations in the ordered vector space of bihyperbolic numbers. Moreover, we state that the set of bihyperbolic numbers form a real Banach algebra with a new defined norm. We introduce conjugates, three hyperbolic valued moduli, real moduli, and multiplicative inverse of the bihyperbolic numbers. We give the concept of the absolute value of a bihyperbolic number which generalizes that of real numbers. Also, we represent the polar form of invertible bihyperbolic numbers.

Cited in 4 Documents

MSC:

30G35 Functions of hypercomplex variables and generalized variables

Keywords:

hyperbolic numbers; bihyperbolic numbers
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\textit{M. Bilgin} and \textit{S. Ersoy}, Adv. Appl. Clifford Algebr. 30, No. 1, Paper No. 13, 17 p. (2020; Zbl 1442.30049)
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References:

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