The resultant of non-commutative polynomials

Abstract

Let $R=K[x;\sigma ]$ be a skew polynomial ring over a division ring$K$. Necessary and sufficient condition under which common rightfactor of two skew polynomials exists is established. It is shownthat the existence of common factor depends on the value ofnon-commutative (Dieudonné) determinant built on coefficients ofpolynomials and their ${\sigma }^l$-images.