The resultant of non-commutative polynomials. (English) Zbl 1199.16047

Erić, Aleksandra Lj.

Mat. Vesn. 60, No. 1, 3-8 (2008).

Let \(K[x,\sigma]\) be a skew polynomial ring over a division ring \(K\) and let \(f,g\in K[x,\sigma]\). The author proves that \(f\) and \(g\) have a common nonunit right factor if and only if there exist polynomials \(c,d\in K[x,\sigma]\) such that \(cf=dg\) and \(\deg c<\deg g\), \(\deg d<\deg f\). She also shows that the existence of common right factor of two polynomials depends on the behaviour of a non-commutative version of resultant of those polynomials.

Reviewer: Andrzej Sladek (Katowice)

MSC:

16S36	Ordinary and skew polynomial rings and semigroup rings
15A15	Determinants, permanents, traces, other special matrix functions
12E05	Polynomials in general fields (irreducibility, etc.)
16U30	Divisibility, noncommutative UFDs

Keywords:

skew polynomials; skew polynomial rings; common right factors; non-commutative resultants