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On the set of zeros of bihyperbolic polynomials

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.