Iterated rings of bounded elements and generalizations of Schmüdgen's Positivstellensatz

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 554, 2003, Pages 19-45

  Schweighofer, Markus ^a  

^a UNIVERSITY OF KONSTANZ   (Germany)

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[No Author keywords available]

Indexed keywords

EID: 0037261914     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.2003.004     Document Type: Article

References (28)

1. [Be1] E. Becker, The real holomorphy ring and sums of 2n-th powers, Géométrie algébrique réelle et formes quadratiques, Lect. Notes Math. 959 (1982), 139-181.
2. [Be2] E. Becker, Extended Artin-Schreier theory of fields, Rocky Mt. J. Math. 14 (1984), 881-897.
3. [BP] E. Becker, V. Powers, Sums of powers in rings and the real holomorphy ring, J. reine angew. Math. 480 (1996), 71-103.
4. [BW] R. Berr, T. Wörmann, Positive polynomials on compact sets, Manuscr. Math. 104 (2001), 135-143.
5. [BCR] J. Bochnak, M. Coste, M.-F. Roy, Géométrie algébrique réelle, Ergeb. Math. Grenzgeb. 12, Springer-Verlag, Berlin 1987.
6. [Bou] N. Bourbaki, Commutative algebra, Hermann, Paris 1972.
7. [Bru] G. Brumfiel, Partially ordered rings and semi-algebraic geometry, London Math. Soc. Lect. Note Ser. 37, Cambridge University Press, Cambridge 1979.
8. [Dri] L. van den Dries, Tame topology and o-minimal structures, London Math. Soc. Lect. Note Ser. 248, Cambridge University Press, Cambridge 1998.
9. [FJ] M. Fried, M. Jarden, Field arithmetic, Ergeb. Math. Grenzgeb. 11, Springer-Verlag, Berlin 1986.
10. [Jac] T. Jacobi, A representation theorem for certain partially ordered commutative rings, Math. Z. 237 (2001), 259-273.
11. [JP] T. Jacobi, A. Prestel, Distinguished representations of strictly positive polynomials, J. reine angew. Math. 532 (2001), 223-235.
12. [KS] M. Knebusch, C. Scheiderer, Einführung in die reelle Algebra, Vieweg Studium 63, Vieweg, Braunschweig 1989.
13. [KM] S. Kuhlmann, M. Marshall, Positivity, sums of squares and the multidimensional moment problem, Transact. AMS, to appear.
14. [Lam] T. Lam, Orderings, valuations and quadratic forms, Reg. Conf. Ser. Math. 52 (1983).
15. [Ma1] M. Marshall, Orderings and real places on commutative rings, J. Algebra 140 (1991), 484-501.
16. [Ma2] M. Marshall, A real holomorphy ring without the Schmüdgen property, Can. Math. Bull. 42 (1999), 354-358.
17. [Ma3] M. Marshall, Positive Polynomials and Sums of Squares, Università di Pisa, Dipart. Mat., Istituti Editoriali e Poligrafici Internaz, 2000.
18. [Ma4] M. Marshall, Extending the Archimedean Positivstellensatz to the non-compact case, Can. Math. Bull. 44 (2001), 223-230.
19. [Ma5] M. Marshall, Approximating positive polynomials using sums of squares, submitted.
20. [Mon] J.-P. Monnier, Anneaux d'holomorphie et Positivstellensatz archimédien, Manuscr. Math. 97 (1998), 269-302.
21. [Pin] S. Pingel, Der reelle Holomorphiering von Algebren, Dissertation, Fernuniversität Hagen 1998.
22. [PD] A. Prestel, C. Delzell, Positive polynomials, Springer Monogr. Math., Berlin 2001.
23. [Sch] K. Schmüdgen, The K-moment problem for compact semi-algebraic sets, Math. Ann. 289, No. 2 (1991), 203-206.
24. [Se1] H.-W. Schülting, On real places of a field and their holomorphy ring, Commun. Algebra 10 (1982), 1239-1284.
25. [Sc2] H.-W. Schülting, Real holomorphy rings in real algebraic geometry, Géométrie algébrique réelle et formes quadratiques, Lect. Notes Math. 959 (1982), 433-442.
26. [Scw] M. Schweighofer, Iterated rings of bounded elements and generalizations of Schmüdgen's theorem, Dissertation, Universität Konstanz 2002.
27. [Sim] O. Simon, Aspects quantitatifs de Nullstellensätze et de Positivstellensätze, Nombres de Pythagore, Commun. Algebra 17 (1989), 637-667.
28. [Ste] G. Stengle, Complexity estimates for the Schmüdgen Positivstellensatz, J. Complexity 12 (1996), 167-174.