Hyperholomorphic functions on commutative algebras

In this article, we study properties of hyperholomorphic functions on commutative
finite-dimensional algebras. The Cauchy–Riemann type conditions for hyperholomorphic
functions is investigated. We prove that a hyperholomorphic function on a commutative finitedimensional
algebra can be expanded in a Taylor series. We also present a technique for
computing zeros of polynomials in commutative algebras.