The Ring of Real-Valued Multivariate Polynomials: An Analyst's Perspective
نویسندگان
چکیده
In this survey we determine an explicit set of generators of the maximal ideals in the ring R[x1, . . . , xn] 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 R[x1, . . . , xn]. 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 R[x1, . . . , xn], which seems to be unknown so far.
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