实值多元多项式环：分析者的观点
The ring of real-valued multivariate polynomials: an analyst's perspective
摘要：
本文确定了实系数$n$变量多项式环$\mathbb R[x_1,\dots,x_n]$中极大理想的生成元的显式集合，并给出了关于$\mathbb R[x_1,\dots,x_n]$的Bass稳定秩的Bass-Vasershtein定理的一个简单的解析证明.证明的成分来自Coquand，Lombardi，Estes和Ohm的不同出版物。我们的结论与计算的拓扑稳定秩的$\mathbb R[x_1,\dots,x_n]$，这似乎是未知的。
英文摘要：
In this survey we determine an explicit set of generators of the maximal ideals in the ring $\mathbb R[x_1,\dots,x_n]$ of polynomials in $n$ variables with real coefficients and give an easy analytic proof of the Bass-Vasershtein theorem on the Bass stable rank of $\mathbb R[x_1,\dots,x_n]$. The ingredients of the proof stem from different publications by Coquand, Lombardi, Estes and Ohm. We conclude with a calculation of the topological stable rank of $\mathbb R[x_1,\dots,x_n]$, which seems to be unknown so far.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
