Аннотация:A skew polynomial ring R = K [x; σ, δ ] is a ring of polynomials with non-commutative multiplication. This creates a difference between left and right divisibility, evaluations, and roots. A polynomial in such a ring may have more roots than its degree, which leads to the concepts of closures and independent sets of roots. In , this leads to the matroids and of right independent and left independent sets, which are isomorphic via the extension of the map φ : [1] → [1] defined by φ (a) = am, where . Extending the field of coefficients of R results in a new ring S of which R is a subring, and if the extension is taken to include roots of an evaluation polynomial of f (x), then all roots of f (x) in S are in the same conjugacy class.
