The ring of real-valued multivariate polynomials: an analyst's perspective
| Autor: | Rudolf Rupp, Raymond Mortini |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM), Fakultaet fuer Mathematik, Universität Ulm - Ulm University [Ulm, Allemagne], Douglas, Krantz, Sawyer, Treil, Wick |
| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
topological stable rank Mathematics::Commutative Algebra Krull dimension Subject Classifications: Primary 46E25 Ring of real polynomials 010102 general mathematics Bass stable rank prime ideals Multivariate polynomials Mathematics - Rings and Algebras 01 natural sciences 010101 applied mathematics Combinatorics Primary 46E25 Secondary 13M10 26C99 Secondary 13M10 Rings and Algebras (math.RA) FOS: Mathematics Krull dimension 0101 mathematics [MATH]Mathematics [math] 26C99 Mathematics Analytic proof |
| Zdroj: | The Corona Problem, connections between operator theory, function theory and geometry The Corona Problem, connections between operator theory, function theory and geometry, Douglas, Krantz, Sawyer, Treil, Wick, 2012, Fields Instiute, Canada. pp.153-176, ⟨10.1007/978-1-4939-1255-1_8⟩ Fields Institute Communications ISBN: 9781493912544 |
| DOI: | 10.48550/arxiv.1402.4832 |
| Popis: | 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. Comment: 20 pages; survey associated with a conference at the Fields institute |
| Databáze: | OpenAIRE |
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