Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On open and closed morphisms between semialgebraic sets
HTML articles powered by AMS MathViewer

by José F. Fernando and J. M. Gamboa PDF
Proc. Amer. Math. Soc. 140 (2012), 1207-1219 Request permission

Abstract:

In this work we study how open and closed semialgebraic maps between two semialgebraic sets extend, via the corresponding spectral maps, to the Zariski and maximal spectra of their respective rings of semialgebraic and bounded semialgebraic functions.
References
  • M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0242802
  • Jacek Bochnak, Michel Coste, and Marie-Françoise Roy, Real algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 36, Springer-Verlag, Berlin, 1998. Translated from the 1987 French original; Revised by the authors. MR 1659509, DOI 10.1007/978-3-662-03718-8
  • G. W. Brumfiel, Quotient spaces for semialgebraic equivalence relations, Math. Z. 195 (1987), no. 1, 69–78. MR 888127, DOI 10.1007/BF01161599
  • J.F. Fernando: On chains of prime ideals in rings of semialgebraic functions. Preprint RAAG (2010). http://www.mat.ucm.es/$\sim$josefer/pdfs/preprint/chains.pdf
  • J.F. Fernando: On distinguished points of the remainder of the semialgebraic Stone–Čech compactification of a semialgebraic set. Preprint RAAG (2010). http://www.mat.ucm.es/$\sim$josefer/pdfs/preprint/remainder.pdf
  • J.F. Fernando, J.M. Gamboa: On the Krull dimension of rings of semialgebraic functions. Preprint RAAG (2010). http://www.mat.ucm.es/$\sim$josefer/pdfs/preprint/dim.pdf
  • J.F. Fernando, J.M. Gamboa: On the spectra of rings of semialgebraic functions. Collectanea Mathematica, to appear. http://www.mat.ucm.es/$\sim$josefer/pdfs/ preprint/spectra.pdf
  • J.F. Fernando, J.M. Gamboa: On Banach-Stone type theorems for semialgebraic sets. Preprint RAAG (2010). http://www.mat.ucm.es/$\sim$josefer/pdfs/preprint/homeo.pdf
  • J.F. Fernando, J.M. Gamboa: On the semialgebraic Stone–Čech compactification of a semialgebraic set. Trans. Amer. Math. Soc. (to appear). http://www.mat.ucm.es/ $\sim$josefer/pdfs/preprint/mspectra.pdf
  • Giuseppe De Marco and Adalberto Orsatti, Commutative rings in which every prime ideal is contained in a unique maximal ideal, Proc. Amer. Math. Soc. 30 (1971), 459–466. MR 282962, DOI 10.1090/S0002-9939-1971-0282962-0
  • M. A. Mulero, Algebraic properties of rings of continuous functions, Fund. Math. 149 (1996), no. 1, 55–66. MR 1372357, DOI 10.4064/fm-149-1-55-66
  • V. Ponomarev, Open mappings of normal spaces, Dokl. Akad. Nauk SSSR 126 (1959), 716–718 (Russian). MR 0107855
  • Claudio Procesi and Gerald Schwarz, Inequalities defining orbit spaces, Invent. Math. 81 (1985), no. 3, 539–554. MR 807071, DOI 10.1007/BF01388587
Similar Articles
Additional Information
  • José F. Fernando
  • Affiliation: Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
  • Email: josefer@mat.ucm.es
  • J. M. Gamboa
  • Affiliation: Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
  • Email: jmgamboa@mat.ucm.es
  • Received by editor(s): July 26, 2010
  • Received by editor(s) in revised form: January 3, 2011
  • Published electronically: August 2, 2011
  • Additional Notes: The authors were supported by the Spanish GAAR MTM2008-00272, Proyecto Santander Complutense PR34/07-15813 and GAAR Grupos UCM 910444
  • Communicated by: Lev Borisov
  • © Copyright 2011 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1207-1219
  • MSC (2010): Primary 14P10, 54C30; Secondary 12D15, 13E99
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10989-4
  • MathSciNet review: 2869106