Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

On the real spectrum of a ring and its application to semialgebraic geometry


Author: Eberhard Becker
Journal: Bull. Amer. Math. Soc. 15 (1986), 19-60
MSC (1985): Primary 14G30, 12D15
DOI: https://doi.org/10.1090/S0273-0979-1986-15431-5
MathSciNet review: 838786
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [A] E. Artin, Über die Zerlegung definiter Funktionen in Quadrate, Hamb. Abh. 5 (1927), 100-115.
  • [B] E. Becker, Valuations and real places in the theory of formally real fields, in [CT-C-M-R], pp. 1-40. MR 683127
  • [Bi] G. Birkhoff, Lattice theory, Amer. Math. Soc., Providence, R.I., 1967.
  • [Bo1] N. Bourbaki, Topologie générale, Chapter 1, Hermann, Paris, 1951.
  • [Bo2] N. Bourbaki, Algébre commutative, Chapter 2, Hermann, Paris, 1961. MR 171800
  • [Br1] L. Bröcker, Positivbereiche in kommutativen Ringen, Abh. Math. Sem. Univ. Hamburg 52 (1982), 170-178. MR 710541
  • [Br2] L. Bröcker, Real spectra and distributions of signature, in [CT-C-M-R], pp. 249-272. MR 683137
  • [Br3] L. Bröcker, Minimale Erzeugung von Positivbereichen, Geom. Dedicata 16 (1984), 335-350. MR 765338
  • [Br4] L. Bröcker, Spaces of orderings and semialgebraic sets, Proc. Conf. on Quadratic and Hermitian Forms (Hamilton 1983), CMS Conf. Proc., vol. 4, Amer. Math. Soc., Providence, R. I., 1984. MR 776457
  • [Bru1] G. W. Brumfiel, Partially ordered rings and semialgebraic geometry, Cambridge, 1979.
  • [Bru2] G. W. Brumfiel, Witt rings and K-theory, Rocky Mountain J. Math. 14 (1984), 733-765. MR 773113
  • [BS] L. Bröcker and J.-H. Schinke, On the L-adic spectrum, preprint, 1986. MR 859868
  • [C] M. Coste, Ensembles semi-algébriques, in [CT-C-M-R], pp. 109-138. MR 683131
  • [CC] M. Coste and M.-F. Coste-Roy, Topologies for real algebraic geometry, in Topos Theoretic Methods in Geometry (A. Kock, ed.) Various Publ. Series 30, Aarhus Universitet, 1979. MR 552658
  • [CC1] M. Coste and M.-F. Coste-Roy, La topologie du spectre réel, Contemporary Math. 8 (1982), 27-60. MR 653174
  • [CR] M.-F. Coste-Roy, Spectre réel d'un anneau et topos étale réel, Thèse Univ. Paris-Nord, 1980.
  • [CT] J.-L. Colliot-Thélène, Variantes du Nullstellensatzz réel et anneaux formellement réels, in [CT-C-M-R], pp. 98-108. MR 683130
  • [CT-C-M-R] J.-L. Colliot-Thélène, M. Coste, L. Mahé and M.-F. Roy, (eds.), Proc. Conf. on "Géométrique Algébrique Réele et Formes Quadratiques", Rennes 1981, Lecture Notes in Math., vol. 959, Springer-Verlag, Berlin and New York, 1982. MR 683126
  • [D] H. Delfs, The homotopy axiom in semialgebraic cohomology, J. Reine Angew. Math. 355 (1985), 108-128. MR 772485
  • [De] C. Delzell, A finiteness theorem for open semi-algebraic sets with applications to Hilbert's 17th problem, Contemporary Math. 8 (1982), 79-97. MR 653176
  • [Dr] L. v. d. Dries, Some applications of a model theoretic fact to (semi-)algebraic geometry, Indag. Math. 44 (1982), 397-401. MR 683527
  • [Du] D. W. Dubois, Real commutative algebra, I. Places, Rev. Mat. Hisp.-Amer. 39 (1979), 57-65. MR 629092
  • [DE] D. Dubois and G. Efroymson, Algebraic theory of real varieties, in Studies and Essays, presented to Yu-Why Chen on his 60th birthday, Taipei 1970, pp. 107-135. MR 280483
  • [DK1] H. Delfs and M. Knebusch, Semialgebraic topology over a real closed field. II, Math. Z. 178 (1981), 175-213. MR 631628
  • [DK2] H. Delfs and M. Knebusch, On the homology of algebraic varieties over real closed fields, J. Reine Angew. Math. 335 (1982), 122-163. MR 667464
  • [DK3] H. Delfs and M. Knebusch, Locally semialgebraic spaces, Lecture Notes in Math., vol. 1173, Springer-Verlag, Berlin and New York, 1985. MR 819737
  • [DR] D. W. Dubois and T. Recio (eds.), Ordered fields and real algebraic geometry, Contemporary Math. 8 (1982). MR 653171
  • [K] I. Kaplansky, Commutative rings, Chicago, 1970. MR 345945
  • [Kn] M. Knebusch, An invitation to real spectra, Proc. Conf. on Quadratic and Hermitian Forms (Hamilton, 1983), CMS Conf. Proc., vol. 4, Amer. Math. Soc., Providence, R. I., 1984. MR 776447
  • [L1] T. Y. Lam, Orderings, valuations and quadratic forms, CBMS Regional Conf. Ser. in Math. no. 52, Amer. Math. Soc., Providence, R.I., 1983. MR 714331
  • [L2] T. Y. Lam, An introduction to real algebra, Rocky Mountain J. Math. 14 (1984), 767-814. MR 773114
  • [La] S. Lang, Algebra, 2nd ed., Addison-Wesley, Reading, Mass., 1967. MR 210527
  • [Lo] S. Lojasiewicz, Ensembles semi-analytiques, multigraphié I.H.E.S., 1965.
  • [Mc] K. McKenna, New facts about Hilbert's 17th problem, Lecture Notes in Math., vol. 498, Springer-Verlag, Berlin and New York, 1975, pp. 220-230. MR 401720
  • [P] A. Prestel, Lectures on formally real fields, Lecture Notes in Math., vol. 1093, Springer-Verlag, Berlin and New York, 1984. MR 769847
  • [PC] S. Priess-Crampe, Angeordnete Strukturen: Gruppen, Körper, projektive Ebenen, Springer, Berlin, Heidelberg and New York, 1983. MR 704186
  • [PR] A. Prestel and P. Roquette, Formally p-adic fields, Lecture Notes in Math., vol. 1050, Springer-Verlag, Berlin and New York, 1984. MR 738076
  • [R] M.-F. Roy, Faisceau structural sur le spectre réel et fonctions de Nash, in [CT-C-M-R], pp. 406-432. MR 683146
  • [S] G. E. Sacks, Saturated model theory, W. A. Benjamin, Inc., Reading, Mass., 1972. MR 398817
  • [S1] N. Schwartz, Der Raum der Zusammenhangskomponenten einer reellen Varietät, Geom. Dedicata 13 (1983), 361-397. MR 699882
  • [S2] N. Schwartz, Real closed spaces, Habilitationsschrift, München, 1984. MR 773144
  • [S3] N. Schwartz, Real closed rings, preprint, 1985. MR 891460
  • [St] G. Stengle, A Nullstellensatz and a Positivstellensatz in semialgebraic geometry, Math. Ann. 207 (1974), 87-97. MR 332747
  • [W] B. L. v. d. Waerden, Algebra. I. 5th ed., Springer-Verlag, Berlin, Göttingen, Heidelberg, 1960.
  • [Wh] H. Whitney, Elementary structure of real algebraic varieties, Ann. of Math. 66 (1957), 545-556. MR 95844
  • [ZS] O. Zariski and P. Samuel, Commutative algebra. II, New York, 1960.

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 14G30, 12D15

Retrieve articles in all journals with MSC (1985): 14G30, 12D15


Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1986-15431-5

American Mathematical Society