Biblioteca de la Universidad Complutense de Madrid

On Open And Closed Morphisms Between Semialgebraic Sets

Impacto

Gamboa, J. M. y Fernando Galván, José Francisco (2012) On Open And Closed Morphisms Between Semialgebraic Sets. Proceedings of the American Mathematical Society, 140 (4). pp. 1207-1219. ISSN 0002-9939

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 2020.

241kB

URL Oficial: http://www.ams.org/journals/proc/2012-140-04/S0002-9939-2011-10989-4/S0002-9939-2011-10989-4.pdf




Resumen

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.


Tipo de documento:Artículo
Palabras clave:Semialgebraic function; semialgebraic set; Zariski spectrum; maximal spectrum; open and closed maps; proper map; Bezoutian; quotient map;Spaces; Rings;Mathematics, Applied; Mathematics
Materias:Ciencias > Matemáticas > Geometria algebraica
Código ID:15166
Referencias:

M.F. Atiyah, I.G. Macdonald: Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ontario: 1969. MR0242802 (39:4129)

J. Bochnak, M. Coste, M.-F. Roy: Real algebraic geometry. Ergeb. Math. 36, Springer- Verlag, Berlin: 1998. MR1659509 (2000a:14067)

G.W. Brumfiel: Quotient spaces for semialgebraic equivalence relations. Math. Z. 195 (1987), no. 1, 69–78. MR888127 (88i:14015)

J.F. Fernando: On chains of prime ideals in rings of semialgebraic functions. Preprint RAAG (2010). http://www.mat.ucm.es/∼josefer/pdfs/preprint/chains.pdf

J.F. Fernando: On distinguished points of the remainder of the semialgebraic Stone–ˇCech compactification of a semialgebraic set. Preprint RAAG (2010). http://www.mat.ucm.es/∼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/∼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/∼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/∼josefer/pdfs/preprint/homeo.pdf

J.F. Fernando, J.M. Gamboa: On the semialgebraic Stone–ˇCech compactification of a semialgebraic set. Trans. Amer. Math. Soc. (to appear). http://www.mat.ucm.es/ ∼josefer/pdfs/preprint/mspectra.pdf

G. De Marco, A. Orsatti: Commutative rings in which every prime ideal is contained in a unique maximal ideal. Proc. Amer. Math. Soc. 30 (1971), no. 3, 459-466. MR0282962 (44:196)

M.-A. Mulero: Algebraic properties of rings of continuous functions. Fund. Math. 149 (1996), no. 1, 55–66. MR1372357 (97c:16038) OPEN AND CLOSED MORPHISMS BETWEEN SEMIALGEBRAIC SETS 1219

V.I. Ponomarev: Open mappings of normal spaces. Dokl. Akad. Nauk SSSR 126 (1959), 716–718. MR0107855 (21:6577)

C. Procesi, G. Schwarz: Inequalities defining orbit spaces. Invent. Math. 81 (1985), no. 3, 539–554. MR807071 (87h:20078) Departamento de ´Algebra, Facultad de Ciencias Matem´aticas, Universidad Complutense de Madrid, 28040 Madrid, Spain E-mail address: josefer@mat.ucm.es Departamento de ´Algebra, Facultad de Ciencias Matem´aticas, Universidad Complutense de Madrid, 28040 Madrid, Spain

Depositado:10 May 2012 08:50
Última Modificación:02 Mar 2016 14:25

Sólo personal del repositorio: página de control del artículo