English

On completion of unimodular rows over polynomial extension of finitely generated rings over $\mathbb{Z}$

Commutative Algebra 2026-03-27 v3

Abstract

In this article, we prove that if RR is a finitely generated ring over Z\mathbb{Z} of dimension d,d2,1d!Rd, d\geq2, \frac{1}{d!}\in R, then any unimodular row over R[X]R[X] of length d+1d+1 can be mapped to a factorial row by elementary transformations.

Keywords

Cite

@article{arxiv.2005.03485,
  title  = {On completion of unimodular rows over polynomial extension of finitely generated rings over $\mathbb{Z}$},
  author = {Sampat Sharma},
  journal= {arXiv preprint arXiv:2005.03485},
  year   = {2026}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2001.05816