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arXiv 2005.034852020-05math.AC

关于多项式扩张有限生成环上单模行的完成

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

Sampat Sharma

备注：: arXiv admin note: substantial text overlap with arXiv:2001.05816

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AI总结：

本文证明在有限生成环R上，若R的维数d≥2且1/d!∈R，则R[X]上的单模行可通过初等变换映射为因子行。

摘要：

本文证明，若R是有限生成环，且R的维数d≥2，且1/d!∈R，则任何R[X]上的长度为d+1的单模行可通过初等变换映射为因子行。

英文摘要：

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

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