The norm of a skew polynomial (Q2149532)

Inspired by the criterion of irreducibility of skew polynomials over a finite field given in [\textit{X. Caruso} and \textit{J. Le Borgne}, J. Symb. Comput. 79, Part 2, 411--443 (2017; Zbl 1373.16046)], this paper investigates some situations where a norm function from a skew polynomial ring over a division ring to a suitable commutative polynomial ring gives information on the factorizations of skew polynomials.