Skip to main content

The real holomorphy ring and sums of 2n-th powers

  • Contributions Des Participants
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 959))

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Becker, E.: Hereditarily pythagorean fields and orderings of higher level. IMPA Lecture Notes, No. 29 (1978), Rio de Janeiro.

    Google Scholar 

  2. Becker, E.: Summen n-ter Potenzen in Körpern, J. reine angew. Mathematik 307/308 (1979), 8–30.

    Google Scholar 

  3. Becker, E.: Partial orders on a field and valuation rings, Comm. Alg. 7 (1979), 1933–1976.

    Article  MathSciNet  MATH  Google Scholar 

  4. Becker, E.: Valuations and real places in the theory of formally real fields, these Proceedings.

    Google Scholar 

  5. Becker, E. and Harman, J. and Rosenberg, A.: Signatures of fields and extension theory, J. reine angew. Mathematik, to appear.

    Google Scholar 

  6. Becker, E. and Köpping, E.: Reduzierte quadratische Formen und Semiordnungen reeller Körper, Abh. Math. Sem. Univ. Hamburg 46 (1977), 143–177.

    Article  MathSciNet  MATH  Google Scholar 

  7. Bröcker, L.: Characterization of fans and hereditarily pythagorean fields, Math. Z. 151 (1976), 149–163.

    Article  MathSciNet  MATH  Google Scholar 

  8. Bröcker, L.: Über die Pythagoraszahl eines Körpers, Arch. Math. 31 (1978), 133–136.

    Article  MATH  Google Scholar 

  9. Diller, J. and Dress, A.: Zur Galoistheorie pythagoreischer Körper, Arch. Math. 16 (1965), 148–152.

    Article  MathSciNet  MATH  Google Scholar 

  10. Ellison, W.J.: Waring’s problem, Amer. Math. Monthly 78 (1971), 10–36.

    Article  MathSciNet  MATH  Google Scholar 

  11. Elman, R. and Lam, T.Y. and Wadsworth, A.: Orderings under field extensions, J. reine angew. Math. 306 (1979), 7–27.

    MathSciNet  MATH  Google Scholar 

  12. Gilmer, R.: Multiplicative ideal theory, Kingston 1968.

    Google Scholar 

  13. Geyer, W.-D.: Galois groups of intersections of local fields, Israel J. Math. 30 (1978), 382–396.

    Article  MathSciNet  MATH  Google Scholar 

  14. Hardy, G.H. and Wright, E.M.: An introduction to the theory of numbers, Oxford 1960.

    Google Scholar 

  15. Hilbert, D.: Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsches Problem), Math. Ann. 67 (1909), 281–300.

    Article  MathSciNet  MATH  Google Scholar 

  16. Heitmann, R.C.: Generating ideals in Prüfer domains, Pac. J. Math. 62 (1976), 117–126.

    Article  MathSciNet  MATH  Google Scholar 

  17. Joly, J.R.: Sommes des puissances d-ièmes dans un anneau commutatif, Acta Arithm. 17 (1970), 37–114.

    MathSciNet  MATH  Google Scholar 

  18. Jacob, B.: On the structure of pythagorean fields, J. Algebra 68 (1981), 247–267.

    Article  MathSciNet  MATH  Google Scholar 

  19. Kamke, E.: Zum Waringschen Problem für rationale Zahlen und Polynome, Math. Ann. 87 (1922), 238–245.

    Article  MathSciNet  MATH  Google Scholar 

  20. Koch, H. and Pieper, H.: Zahlentheorie. Ausgewählte Methoden und Ergebnisse, Berlin 1976.

    MATH  Google Scholar 

  21. Knebusch, M.: On the extension of real places, Comment. Math. Helv. 48 (1973), 354–369.

    Article  MathSciNet  MATH  Google Scholar 

  22. Lam, T.Y.: The algebraic theory of quadratic forms, Reading 1973.

    Google Scholar 

  23. Lam, T.Y.: The theory of ordered fields, in: Proceedings of the Algebra and Ring Theory Conference (ed. B. Mc Donald), Univ. of Oklahoma 1979, Lect. Not. in Pure and App. Math. Vol. 55.

    Google Scholar 

  24. Schülting, H.-W.: Über reelle Stellen eines Körpers und ihren Holomorphiering, Ph.D. thesis, Dortmund 1979.

    Google Scholar 

  25. Schülting, H.-W.: On real places of a field and their holomorphy ring, Comm. Alg., to appear.

    Google Scholar 

  26. Schülting, H.-W.: Über die Erzeugendenzahl invertierbarer Ideale in Prüferringen, Comm. Alg. 7 (1979), 1331–1349.

    Article  MATH  Google Scholar 

  27. Siegel, C.L.: Darstellung total positiver Zahlen durch Quadrate, Math. Z. 11 (1921), 246–275.

    Article  MathSciNet  MATH  Google Scholar 

  28. Zariski, O. and Samuel, P.: Commutative algebra II, New York 1960.

    Google Scholar 

Added in proof

  1. Jacob, B.: Fans, real valuations and hereditarily-Pythagorean fields, Pac. J. Math. 93 (1981), 95–105.

    Article  MathSciNet  MATH  Google Scholar 

  2. Pourchet, Y.: Sur la représentation en somme de carrés des polynômes à une indéterminée sur un corps de nombres algébriques, Acta Arithm. 19 (1971), 89–104.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jean-Louis Colliot-Thélène Michel Coste Louis Mahé Marie-Françoise Roy

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Becker, E. (1982). The real holomorphy ring and sums of 2n-th powers. In: Colliot-Thélène, JL., Coste, M., Mahé, L., Roy, MF. (eds) Géométrie Algébrique Réelle et Formes Quadratiques. Lecture Notes in Mathematics, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062253

Download citation

  • DOI: https://doi.org/10.1007/BFb0062253

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11959-3

  • Online ISBN: 978-3-540-39548-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics