no. 1
On global Nash functions
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 27 (1994) no. 1, pp. 103-124. 
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     author = {Ruiz, Jes\'us M. and Shiota, Masahiro},
     title = {On global {Nash} functions},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {103--124},
     publisher = {Elsevier},
     volume = {Ser. 4, 27},
     number = {1},
     year = {1994},
     doi = {10.24033/asens.1690},
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     zbl = {0805.14027},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.1690/}
}
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Ruiz, Jesús M.; Shiota, Masahiro. On global Nash functions. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 27 (1994) no. 1, pp. 103-124. doi : 10.24033/asens.1690. http://archive.numdam.org/articles/10.24033/asens.1690/

[AnBrRz1] C. Andradas, L. Bröcker and J. M. Ruiz, Minimal Generation of Basic Open Semianalytic Sets (Invent. Math., Vol. 92, 1988, pp. 409-430). | MR | Zbl

[AnBrRz2] C. Andradas, L. Bröcker and J. M. Ruiz, Real Algebra and Analytic Geometry, in preparation.

[Ar] M. Artin, On the Solutions of Analytic Equations (Invent. Math., Vol. 5, 1988, pp. 277-291). | MR | Zbl

[BT] L. Beretta and A. Tognoli, Nash Sets and Global Equations (Bollettino U.M.I., Vol. 7, 1990, pp. 31-44). | MR | Zbl

[BCR] J. Bochnak, M. Coste and M.-F. Roy, Géométrie algébrique réelle (Ergeb. Math., Vol. 12, Springer-Verlag, Berlin-Heidelberg-New York, 1987). | MR | Zbl

[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). | MR | Zbl

[Bk] N. Bourbaki, Commutative Algebra, Hermann, Paris, 1972. | MR

[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). | MR | Zbl

[Br2] L. Bröcker, On Basic Semialgebraic Sets (Expo. Math., Vol. 9, 1991, pp. 289-334). | MR | Zbl

[BrWh] F. Bruhat and H. Whitney, Quelques propriétés fondamentales des ensembles analytiques réels (Comment. Math. Helv., Vol. 33, 1959, pp. 132-160). | MR | Zbl

[C] H. Cartan, Variétés analytiques réelles et variétés analytiques complexes (Bull. Soc. Math. France, Vol. 85, 1957, pp. 77-99). | Numdam | MR | Zbl

[CtDp] M. Coste and C. Diop, Problems About Nash Functions, talk in Reelle algebraische Geometrie, Oberwolfach, June 1990.

[vdD] L. Van Den Dries, Model Theory of Fields (Thesis, Utrecht, 1978).

[Ef1] G. Efroymson, Nash Rings in Planar Domains (Trans. Amer. Math. Soc., Vol. 249, 1979, pp. 435-445). | MR | Zbl

[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). | MR | Zbl

[En] O. Endler, Valuation Theory, Universitext, Springer-Verlag, Berlin-Heidelberg-New York, 1970. | Zbl

[Lm] T. Y. Lam, Orderings, Valuations and Quadratic Forms (Reg. Conf. Math., Vol. 52, AMS, 1983). | MR | Zbl

[Mt] H. Matsumura, Commutative Algebra, second edition (Math. Lecture Note Series, Vol. 56, Benjamin, London-Amsterdam-Tokyo, 1980). | MR | Zbl

[Ng] M. Nagata, Local Rings (Intersc. Tracts Math., Vol. 13, John Wiley & Sons, New York-London, 1962). | MR | Zbl

[Pk] D. Pecker, On Efroymson's Extension Theorem for Nash Functions (J. Pure Appl. Algebra, Vol. 37, 1985, pp. 193-203). | MR | Zbl

[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). | MR | Zbl

[Rt] Ch. Rotthaus, On the Approximation Property of Excellent Rings (Invent. Math., Vol. 88, 1987, p. 39-63). | MR | Zbl

[Rz1] J. M. Ruiz, On Hilbert's 17th Problem and Real Nullstellensatz for Global Analytic Functions (Math. Z., Vol. 190, 1985, pp. 447-459). | MR | Zbl

[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). | Numdam | MR | Zbl

[Rz3] J. M. Ruiz, A Going-Down Theorem for Real Spectra (J. of Algebra, Vol. 124, No. 2, 1989, pp. 278-283). | MR | Zbl

[RzSh] J. M. Ruiz and M. Shiota, Equivalence of Important Problems on Nash Functions (to appear).

[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. | MR | Zbl

[Sh2] M. Shiota, Nash Manifolds (Lecture notes in Math., No. 1269, Springer-Verlag, Berlin-Heidelberg-New York, 1987). | MR | Zbl

[Sh3] M. Shiota, Extension et factorisation de fonctions de Nash C∞ (C. R. Acad. Sci. Paris, Vol. 308, Séries I, 1989, pp. 253-256). | MR | Zbl

[TT] A. Tancredi and A. Tognoli, On the Extension of Nash Functions (Math. Ann., Vol. 288, 1990, pp. 595-604). | MR | Zbl

[Tg] J.-C. Tougeron, Idéaux de fonctions différentiables (Ergeb. Math., Vol. 71, Springer-Verlag, Berlin-Heidelberg-New York, 1972). | MR | Zbl

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