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

Fajardo William, Lezama Oswaldo

Fundamenta Informaticae

2019

Vol. 164, nr 1

41--59

In this short note we present an elementary matrix-constructive algorithmic proof of the Quillen-Suslin theorem for Ore extensions A := K[x; σ, δ], where K is a division ring, σ : K → K is a division ring automorphism and σ : K → K is a σ-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.