On Stably free modules over Laurent polynomial rings

TL;DR

This paper proves that over Laurent polynomial rings with a finite-dimensional commutative base ring, all stably free modules of sufficiently high rank are free, establishing a Hermite property for these rings.

Contribution

It provides a constructive proof that stably free modules over Laurent polynomial rings are free when their rank exceeds the dimension of the base ring.

Findings

All stably free modules over R[X;X^{-1}] of rank > dim R are free.

R[X;X^{-1}] is (dim R)-Hermite.

Constructive proof approach used.

Abstract

We prove constructively that for any finite-dimensional commu- tative ring R, every stably free module over R[X;X^{1}] of rank > dim R is free, i.e., R[X;X^{-1}] is (dimR)-Hermite.