On the spectra of rings of semialgebraic functions

DOI10.1007/s13348-011-0041-0zbMath1291.14085OpenAlexW1965985323MaRDI QIDQ1956304

José F. Fernando, Jose Manuel Gamboa

Publication date: 13 June 2013

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13348-011-0041-0

zbMATH Keywords

semialgebraic setrings of continuous functionsradical idealfunctorialitylocal compactness\(z\)-idealsemialgebraic functionmaximal spectrumLojasiewicz inequalitysemialgebraic depthZariski spectrumcurve selection lemmagoing up lemmaNash diffeomorphismTietze Urysohn extension

Mathematics Subject Classification ID

Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Semialgebraic sets and related spaces (14P10) Extension of maps (54C20) Real-valued functions in general topology (54C30) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (4)

On the remainder of the semialgebraic Stone-Čech compactification of a semialgebraic set ⋮ 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

Cites Work

• On Łojasiewicz's inequality and the nullstellensatz for rings of semialgebraic functions
• Real closed rings. II. Model theory
• Separation, retractions and homotopy extension in semialgebraic spaces
• On the Krull dimension of rings of continuous semialgebraic functions
• On the semialgebraic Stone–Čech compactification of a semialgebraic set
• The basic theory of real closed spaces
• Real closed rings, I. Residue rings of rings of continuous functions
• Smooth points of a semialgebraic set
• Commutative Rings in Which Every Prime Ideal is Contained in a Unique Maximal Ideal
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