论文标题
在完成有限生成的环的多项式扩展上，$ \ mathbb {z} $完成了单模型的行。
On completion of unimodular rows over polynomial extension of finitely generated rings over $\mathbb{Z}$
论文作者
论文摘要
在本文中，我们证明，如果$ r $是$ \ mathbb {z} $的有限生成的戒指，$ d，d \ geq2，\ frac {1} {d！} \ in r $中，则在$ d $ d+1 $的长度$ r [x]上的任何单模型的行都可以映射到element yeartory cortressation consorcation croworeal consorly roworeal crowsory croworeal crowitions roworeal crowsional crowistation。
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.
