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

Abstract

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, $\sigma: K \to K$ is a division ring automorphism and $\sigma: K \to K$ is a $\sigma$-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.

William A. Fajardo

Instructor