The Hermite ring conjecture in dimension one

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• 作者：Ihsen Yengui
• 关键词：Stably free modules ; Unimodular rows ; Quillen– ; Suslin theorem ; Hermite rings ; Hermite ring conjecture ; Constructive mathematics
• 刊名：Journal of Algebra
• 出版年：2008
• 出版时间：1 July 2008
• 年：2008
• 卷：320
• 期：1
• 页码：437-441
• 全文大小：101 K

文摘

We prove constructively that for any ring R of Krull dimension 1 and n3, the group E_n(R[X]) acts transitively on Um_n(R[X]). In particular, we obtain that for any ring R with Krull dimension 1, all finitely generated stably free modules over R[X] are free. This settles the long-standing Hermite ring conjecture for rings of Krull dimension 1.