RT Journal Article
T1 On the spectra of rings of semialgebraic functions
A1 Fernando Galván, José Francisco
A1 Gamboa Mutuberria, José Manuel
AB 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.
PB Springer
SN 0010-0757
YR 2012
FD 2012
LK https://hdl.handle.net/20.500.14352/42319
UL https://hdl.handle.net/20.500.14352/42319
LA eng
NO 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) 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 RAAG, 2010) 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 (preprint RAAG, 2010) 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 (preprint RAAG, 2010) 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 (preprint RAAG, 2010) 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 (preprint RAAG, 2010) Fernando, J.F., Gamboa, J.M.: On the semialgebraic Stone–Čech compactification of a semialgebraic set. Transactions of AMS. http://www.ams.org/cgi-bin/mstrack/accepted_papers?jrnl=tran (2010, accepted) Gillman, L., Jerison, M.: Rings of continuous functions. The University Series in Higher Nathematics, vol. 1. D. Van Nostrand Company, Inc., Princeton (1960) 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), 459–466 (1971) 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)
NO GAAR Español
NO Proyecto Santander-Complutense
NO GAAR Grupos UCM
DS Docta Complutense
RD 29 abr 2024