Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.


Sur le 17ème problème de Hilbert pour les fonctions de Nash
HTML articles powered by AMS MathViewer

by Jacek Bochnak PDF
Proc. Amer. Math. Soc. 71 (1978), 183-188 Request permission


The purpose of this note is to give a more refined version of a theorem of Efroymson: If $U \subset {{\mathbf {R}}^n}$ is defined by polynomial inequalities of the form ${f_i} > 0,i = 1, \ldots ,p$, and if g is a positive definite Nash function on U, then g is a finite sum of squares of Nash meromorphe functions on U.
  • Emil Artin, The collected papers of Emil Artin, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1965. Edited by Serge Lang and John T. Tate. MR 0176888, DOI 10.1007/978-1-4614-6294-1
  • Jacek Bochnak, Sur la factorialité des anneaux de fonctions de Nash, Comment. Math. Helv. 52 (1977), no. 2, 211–218 (French). MR 457763, DOI 10.1007/BF02567365
  • J. Bochnak and J.-J. Risler, Le théorème des zéros pour les variétés analytiques réelles de dimension $2$, Ann. Sci. École Norm. Sup. (4) 8 (1975), no. 3, 353–363. MR 396994, DOI 10.24033/asens.1292
  • Paul J. Cohen, Decision procedures for real and $p$-adic fields, Comm. Pure Appl. Math. 22 (1969), 131–151. MR 244025, DOI 10.1002/cpa.3160220202
  • Gustave A. Efroymson, A Nullstellensatz for Nash rings, Pacific J. Math. 54 (1974), 101–112. MR 360576, DOI 10.2140/pjm.1974.54.101
  • Gustave Efroymson, Substitution in Nash functions, Pacific J. Math. 63 (1976), no. 1, 137–145. MR 409456, DOI 10.2140/pjm.1976.63.137
  • D. Gondard, Le 17ème problème de Hilbert, Thèse du 3ème cycle, Paris Orsay 1974. S. Land, Algèbre, Addison-Wesley, Reading, Mass., 1965.
  • Tadeusz Mostowski, Some properties of the ring of Nash functions, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), no. 2, 245–266. MR 412180
  • Albrecht Pfister, Hilbert’s seventeenth problem and related problems on definite forms, Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Northern Illinois Univ., De Kalb, Ill., 1974) Amer. Math. Soc., Providence, R.I., 1976, pp. 483–489. MR 0424679
  • J.-J. Risler, Les théorèmes des zeros en géométries algébrique et analytique réelles, Bull. Soc. Math. France 104 (1976), 113-127. N. Bourbaki, Algèbre, Chapitre 6, Groupes et corps ordonnés, $\S 2$, Hermann, Paris, 1952.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32B05, 12D99
  • Retrieve articles in all journals with MSC: 32B05, 12D99
Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 183-188
  • MSC: Primary 32B05; Secondary 12D99
  • DOI:
  • MathSciNet review: 0486597