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Keywords:
Quillen-Suslin theorem; stably free module; Hermite ring conjecture; Laurent polynomial ring; constructive mathematics
Quillen-Suslin theorem; stably free module; Hermite ring conjecture; Laurent polynomial ring; constructive mathematics
Summary:
We prove that for any ring ${\bf R}$ of Krull dimension not greater than 1 and $n\geq 3$, the group ${\rm E}_{n}({\bf R}[X, X^{-1}])$ acts transitively on ${\rm Um}_{n}({\bf R} [X, X^{-1}])$. In particular, we obtain that for any ring ${\bf R}$ with Krull dimension not greater than 1, all finitely generated stably free modules over ${\bf R} [X, X^{-1}]$ are free. All the obtained results are proved constructively.
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