The Hermite ring conjecture in dimension one

JOURNAL OF ALGEBRA

卷:320

Article

Yengui, Ihsen

关键词: stably free modules;    unimodular rows;    Quillen-Suslin theorem;    Hermite rings;    Hermite ring conjecture;    constructive mathematics;   

DOI  :  10.1016/j.jalgebra.2008.02.007

来源: Elsevier

【 摘 要 】

We prove constructively that for any ring R of Krull dimension <= 1 and n >= 3, 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. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free