On global Nash functions

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1. [AnBrRz1] C. ANDRADAS, L. BRÖCKER and J. M. RUIZ, Minimal Generation of Basic Open Semianalytic Sets (Invent. Math., Vol. 92, 1988, pp. 409-430). Zbl0655.32011MR89f:32016
2. [AnBrRz2] C. ANDRADAS, L. BRÖCKER and J. M. RUIZ, Real Algebra and Analytic Geometry, in preparation. 
3. [Ar] M. ARTIN, On the Solutions of Analytic Equations (Invent. Math., Vol. 5, 1988, pp. 277-291). Zbl0172.05301MR38 #344
4. [BT] L. BERETTA and A. TOGNOLI, Nash Sets and Global Equations (Bollettino U.M.I., Vol. 7, 1990, pp. 31-44). Zbl0735.14037MR91b:58001
5. [BCR] J. BOCHNAK, M. COSTE and M.-F. ROY, Géométrie algébrique réelle (Ergeb. Math., Vol. 12, Springer-Verlag, Berlin-Heidelberg-New York, 1987). Zbl0633.14016MR90b:14030
6. [BE] J. BOCHNAK and G. EFROYMSON, An Introduction to Nash Functions, in Géométrie algébrique réelle et formes quadratiques, pp. 41-54 (Lecture Notes in Math., No. 959, Springer-Verlag, Berlin-Heidelberg-New York, 1982). Zbl0516.14019MR84b:32013
7. [Bk] N. BOURBAKI, Commutative Algebra, Hermann, Paris, 1972. MR50 #12997
8. [Br1] L. BRÖCKER, On the Stability Index of Noetherian Rings, in Real Analytic and Algebraic Geometry, pp. 72-80 (Lecture Notes in Math., No. 1420, Springer-Verlag, Berlin-Heidelberg-New York, 1990). Zbl0696.13011MR91g:14055
9. [Br2] L. BRÖCKER, On Basic Semialgebraic Sets (Expo. Math., Vol. 9, 1991, pp. 289-334). Zbl0783.14035MR93b:14085
10. [BrWh] F. BRUHAT and H. WHITNEY, Quelques propriétés fondamentales des ensembles analytiques réels (Comment. Math. Helv., Vol. 33, 1959, pp. 132-160). Zbl0100.08101MR21 #889
11. [C] H. CARTAN, Variétés analytiques réelles et variétés analytiques complexes (Bull. Soc. Math. France, Vol. 85, 1957, pp. 77-99). Zbl0083.30502MR20 #1339
12. [CtDp] M. COSTE and C. DIOP, Problems About Nash Functions, talk in Reelle algebraische Geometrie, Oberwolfach, June 1990. 
13. [vdD] L. VAN DEN DRIES, Model Theory of Fields (Thesis, Utrecht, 1978). 
14. [Ef1] G. EFROYMSON, Nash Rings in Planar Domains (Trans. Amer. Math. Soc., Vol. 249, 1979, pp. 435-445). Zbl0426.14024MR80b:14018
15. [Ef2] G. EFROYMSON, The Extension Theorem for Nash Functions, in Géométrie algébrique réelle et formes quadratiques, pp. 343-357 (Lecture Notes in Math., No. 959, Springer-Verlag, Berlin-Heidelberg-New York 1982). Zbl0516.14020MR84i:58002
16. [En] O. ENDLER, Valuation Theory, Universitext, Springer-Verlag, Berlin-Heidelberg-New York, 1970. Zbl0257.12111
17. [Lm] T. Y. LAM, Orderings, Valuations and Quadratic Forms (Reg. Conf. Math., Vol. 52, AMS, 1983). Zbl0516.12001MR85e:11024
18. [Mt] H. MATSUMURA, Commutative Algebra, second edition (Math. Lecture Note Series, Vol. 56, Benjamin, London-Amsterdam-Tokyo, 1980). Zbl0441.13001MR82i:13003
19. [Ng] M. NAGATA, Local Rings (Intersc. Tracts Math., Vol. 13, John Wiley & Sons, New York-London, 1962). Zbl0123.03402MR27 #5790
20. [Pk] D. PECKER, On Efroymson's Extension Theorem for Nash Functions (J. Pure Appl. Algebra, Vol. 37, 1985, pp. 193-203). Zbl0581.14016MR87e:58002
21. [Pr] A. PRESTEL, Pseudo Real Closed Fields, in Set Theory and Model Theory, pp. 127-156 (Lecture Notes in Math., No. 872, Springer-Verlag, Berlin-Heidelberg-New York 1981). Zbl0466.12018MR84b:12032
22. [Rt] Ch. ROTTHAUS, On the Approximation Property of Excellent Rings (Invent. Math., Vol. 88, 1987, p. 39-63). Zbl0614.13014MR88c:14005
23. [Rz1] J. M. RUIZ, On Hilbert's 17th Problem and Real Nullstellensatz for Global Analytic Functions (Math. Z., Vol. 190, 1985, pp. 447-459). Zbl0579.14021MR87b:32010
24. [Rz2] J. M. RUIZ, On the Real Spectrum of a Ring of Global Analytic Functions (Publ. Inst. Recherche Math. Rennes, Vol. 4, 1986, pp. 84-95). Zbl0634.14015MR91e:14050
25. [Rz3] J. M. RUIZ, A Going-Down Theorem for Real Spectra (J. of Algebra, Vol. 124, No. 2, 1989, pp. 278-283). Zbl0688.14020MR91g:14056
26. [RzSh] J. M. RUIZ and M. SHIOTA, Equivalence of Important Problems on Nash Functions (to appear). 
27. [Sh1] M. SHIOTA, Sur la factorialité de l'anneau des fonctions lisses rationnelles (C. R. Acad. Sci. Paris, Vol. 292, Séries I, 1981, pp. 67-70. Zbl0489.14013MR82b:14009
28. [Sh2] M. SHIOTA, Nash Manifolds (Lecture notes in Math., No. 1269, Springer-Verlag, Berlin-Heidelberg-New York, 1987). Zbl0629.58002MR89b:58011
29. [Sh3] M. SHIOTA, Extension et factorisation de fonctions de Nash C∞ (C. R. Acad. Sci. Paris, Vol. 308, Séries I, 1989, pp. 253-256). Zbl0681.32006MR90h:32017
30. [TT] A. TANCREDI and A. TOGNOLI, On the Extension of Nash Functions (Math. Ann., Vol. 288, 1990, pp. 595-604). Zbl0699.32006MR92c:32011
31. [Tg] J.-C. TOUGERON, Idéaux de fonctions différentiables (Ergeb. Math., Vol. 71, Springer-Verlag, Berlin-Heidelberg-New York, 1972). Zbl0251.58001MR55 #13472

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