  In this paper motivated by the celebrated fundamental theorem of algebra and
its standard proof utilizing Liouville's Theorem, we prove the fundamental
theorem of algebra type results for both commutative and noncommutative
polynomials in the setting of left (resp. right) alternative topological
complex algebras whose topological duals separates their elements and that of
such real algebras whose centers contain certain copies of complex numbers. An
application of one of the main results of the paper is the existence of
eigenvalues for matrices with entries from arbitrary finite-dimensional complex
algebras. We also prove the existence of right eigenvalues for matrices with
entries from finite-dimensional associative real algebras that contain copies
of the complex numbers.
