Resultants of skew polynomials over division rings

Abstract

Let $\mathbb{F}$ be a division ring. In this paper, we extent some of the main well-known results about the resultant of two univariate polynomials to the more general context of an Ore extension $\mathbb{F}[x;\sigma,\delta]$. Finally, some algorithms and Magma programs are given as a numerical application of the main theoretical results of this paper.