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arXiv · 1402.4832

The ring of real-valued multivariate polynomials: an analyst's perspective

Raymond Mortini·Rudolf Rupp
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Abstract

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.

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Raymond Mortini, Rudolf Rupp. 2014-02-19. The ring of real-valued multivariate polynomials: an analyst's perspective. https://arxiv.org/abs/1402.4832

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