On the set of zeros of bihyperbolic polynomials

Abstract

Abstract Extensions of basic complex numbers to higher dimensions have a renewed interest in mathematics, physics, and engineering because of fruitful applications. Quaternions is one of the most popular sets of tetranumbers, however, they form a non-commutative algebra. A couple of interesting commutative algebras of tetranumbers are defined by bicomplex and bihyperbolic numbers. Bicomplex numbers are a natural extension of complex numbers, whereas bihyperbolic numbers are a natural extension of hyperbolic numbers to four dimensions. In this article, we study the roots of polynomials having coefficients belonging to the tetranumbers commutative algebra of bihyperbolic numbers. Keywords: bihyperbolic numberspolynomialszerosAMS Subject Classifications: 30C1512D10 Acknowledgement This work was completed with the support of the State Fund for Fundamental Researches of Ukraine, Project No. 25, 1/084, and the Chair on Telecommunications at Tecnológico de Monterrey.