On the Krull dimension of rings of continuous semialgebraic functions

DOI10.4171/RMI/852zbMath1362.14059arXiv1306.4109OpenAlexW2224388778MaRDI QIDQ888918

José F. Fernando, Jose Manuel Gamboa

Publication date: 3 November 2015

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.4109

zbMATH Keywords

Krull dimensiontranscendence degreelocal dimensionreal closed field\(z\)-idealbounded continuous semialgebraic functioncontinuous semialgebraic functionsemialgebraic depth

Mathematics Subject Classification ID

Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Semialgebraic sets and related spaces (14P10) Real-valued functions in general topology (54C30) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (7)

On the remainder of the semialgebraic Stone-Čech compactification of a semialgebraic set ⋮ Global Łojasiewicz inequalities on comparing the rate of growth of polynomial functions ⋮ On the spectra of rings of semialgebraic functions ⋮ On open and closed morphisms between semialgebraic sets ⋮ On the size of the fibers of spectral maps induced by semialgebraic embeddings ⋮ Spectral maps associated to semialgebraic branched coverings ⋮ On the semialgebraic Stone–Čech compactification of a semialgebraic set

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