Elementary Matrix-computational Proof of Quillen-Suslin Theorem for Ore Extensions

摘要

In this short note we present an elementary matrix-constructive algorithmic proof of the Quillen-Suslin theorem for Ore extensions A := K [x; sigma, delta], where K is a division ring, sigma : K - K is a division ring automorphism and delta : K - K is a a-derivation of K. It asserts that every finitely generated projective A-module is free. We construct a symbolic algorithm that computes the basis of a given finitely generated projective A-module. The algorithm is implemented in a computational package. Its efficiency is illustrated by four representative examples.