On the spectra of rings of semialgebraic functions

• Autores: José Francisco Fernando Galván , J.M. Gamboa
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 63, Fasc. 3, 2012, págs. 299-331
• Idioma: inglés
• DOI: 10.1007/s13348-011-0041-0
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this article we study the most significant algebraic, topological and functorial properties of the Zariski and maximal spectra of rings of semialgebraic and bounded semialgebraic functions on a semialgebraic set.

• Referencias bibliográficas
  • Bochnak, J., Coste, M., Roy, M.-F.: Real Algebraic Geometry. Ergeb. Math., vol. 36. Springer, Berlin (1998)
  • Bourbaki, N.: General Topology, chapters 1–4. Elements of Mathematics. Springer, Berlin (1989)
  • Birkhoff G., Pierce R.S.: Lattice-ordered rings. An. Acad. Brasil. Ci. 28, 41–69 (1956)
  • Cherlin G.-L., Dickmann M.A.: Real closed rings. I. Residue rings of rings of continuous functions. Fund. Math. 126(2), 147–183 (1986)
  • Cherlin G.-L., Dickmann M.A.: Real closed rings. II. Model theory. Ann. Pure Appl. Log. 25(3), 213–231 (1983)
  • De Marco G., Orsatti A.: Commutative rings in which every prime ideal is contained in a unique maximal ideal. Proc. Am. Math. Soc. 30(3),...
  • Delfs H., Knebusch M.: Separation, retractions and homotopy extension in semialgebraic spaces. Pac. J. Math. 114(1), 47–71 (1984)
  • Fernando, J.F.: On chains of prime ideals in rings of semialgebraic functions. http://www.mat.ucm.es/~josefer/pdfs/preprint/chains.pdf (preprint...
  • Fernando, J.F.: On distinguished points of the remainder of the semialgebraic Stone–Čech compactification of a semialgebraic set. http://www.mat.ucm.es/~josefer/pdfs/preprint/remainder.pdf...
  • Fernando, J.F.: On the fibers of semialgebraic spectral maps. http://www.mat.ucm.es/~josefer/pdfs/preprint/fibers.pdf (preprint RAAG, 2010)
  • Fernando, J.F., Gamboa, J.M.: On Łojasiewicz’s inequality and the Nullstellensatz for rings of semialgebraic functions. http://www.mat.ucm.es/~josefer/pdfs/preprint/null-loj.pdf...
  • Fernando, J.F., Gamboa, J.M.: On the Krull dimension of rings of semialgebraic functions. http://www.mat.ucm.es/~josefer/pdfs/preprint/dim.pdf...
  • Fernando, J.F., Gamboa, J.M.: On Banach-Stone type theorems in the semialgebraic setting. http://www.mat.ucm.es/~josefer/pdfs/preprint/homeo.pdf...
  • Fernando, J.F., Gamboa, J.M.: On the semialgebraic Stone–Čech compactification of a semialgebraic set. Transactions of AMS. http://www.ams.org.sire.ub.edu/cgi-bin/mstrack/accepted_papers?jrnl=tran...
  • Gillman, L., Jerison, M.: Rings of continuous functions. The University Series in Higher Nathematics, vol. 1. D. Van Nostrand Company, Inc.,...
  • Schwartz, N.: Real closed spaces. Ordered fields and real algebraic geometry (Boulder, Colo., 1983). Rocky Mt. J. Math. 14(4), 971–972 (1984)
  • Schwartz, N.: The basic theory of real closed spaces. Mem. Am. Math. Soc. 77(397) (1989)
  • Stasica J.: Smooth points of a semialgebraic set. Ann. Polon. Math. 82(2), 149–153 (2003)