On the action of the elementary group on the unimodular rows

JOURNAL OF ALGEBRA

卷:368

Article

Abedelfatah, Abed

关键词: Stably free modules;    Hermite rings;    Unimodular rows;    Laurent polynomial rings;   

DOI  :  10.1016/j.jalgebra.2012.05.026

来源: Elsevier

【 摘 要 】

We prove that for any commutative ring R of Krull dimension zero. n >= 3 and A = R[X-1(+/- 1) , . . . , X-k(+/- 1), Xk+1, . . . , X-m], the group E-n(A) acts transitively on Um(n)(A). In particular, we obtain that every stably free module over A is free, i.e., A is Hermite ring. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free