Factoring skew polynomials over Hamilton's quaternion algebra and the complex numbers

Using nonassociative algebras constructed out of skew-polynomial rings as introduced by Petit, we show that all non-constant polynomials in the skew-polynomial ring over Hamilton's quaternions decompose into a product of linear factors, and that all non-constant polynomials in the skew-polynomial ring over the complex numbers decompose into a product of linear and quadratic irreducible factors.

S. Pumpluen < susanne.pumpluen@nottingham.ac.uk >