The resultant of non-commutative polynomials

Aleksandra Lj. EriŠ

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