Skip to main content

Nonstandard aspects of Hilbert's irreducibility theorem

  • Contributed Papers
  • Conference paper
  • First Online:
Book cover Model Theory and Algebra

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 498))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. DÖRGE, K. Zum Hilbertschen Irreduzibilitätssatz. Math. Ann. 95 (1926) 84–97

    Article  MathSciNet  MATH  Google Scholar 

  2. DÖRGE, K. Einfacher Beweis des Hilbertschen Irreduzibilitätssatzes. Math. Ann. 96 (1926), 176–182.

    Article  MATH  Google Scholar 

  3. EICHLER, M. Zum Hilbertschen Irreduzibilitätssatz. Math. Ann. 116 (1939), 742–748

    Article  MathSciNet  MATH  Google Scholar 

  4. FRANZ, W. Untersuchungen zum Hilbertschen Irreduzibilitätssatz. Math. Z. 33 (1931), 275–293

    Article  MathSciNet  MATH  Google Scholar 

  5. FRIED, M. On Hilbert's irreducibility theorem. J. Number Theory 6 (1974), 211–231

    Article  MathSciNet  MATH  Google Scholar 

  6. FRIED, M.—LEWIS, D. J. Solution spaces for Diophantine Problems, Chap. IV. (Mimeographed Notes).

    Google Scholar 

  7. GILMORE, P.C.—ROBINSON, A. Metamathematical considerations on the relative irreducibility of polynomials. Canad. J. Math. 7 (1955), 483–489

    Article  MathSciNet  MATH  Google Scholar 

  8. HILBERT, D. Über die Irreduzibilität ganzer rationaler Funktionen mit ganzzahligen Koeffizienten. Crelles J. 110 (1892), 104–129

    MathSciNet  MATH  Google Scholar 

  9. INABA, E. Über den Hilbertschen Irreduzibilitätssatz. Japan. J. Math. 19 (1944), 1–25.

    MathSciNet  MATH  Google Scholar 

  10. KNOBLOCH, H.W. Zum Hilbertschen Irreduzibilitätssatz. Abh. Math. Sem. Univ. Hamburg 19 (1955), 176–190

    Article  MathSciNet  MATH  Google Scholar 

  11. KOCHEN, S. Abraham Robinson, Memorial Service, Sep. 15 (1974). (Mimeographed Copy).

    Google Scholar 

  12. KUYK, W. Generic approach to the Galois embedding and extension problem. J. Algebra 9 (1968), 393–407

    Article  MathSciNet  MATH  Google Scholar 

  13. KUYK, W. Extensions de corps hilbertiens. J. Algebra 14 (1970), 112–124

    Article  MathSciNet  MATH  Google Scholar 

  14. LANG, S. Some applications of the local uniformization theorem. Amer. J. Math. 76 (1954), 362–374

    Article  MathSciNet  MATH  Google Scholar 

  15. LANG, S. Introduction to Algebraic Geometry (New York-London 1958).

    Google Scholar 

  16. LANG, S. Le théorème d'irréductibilité de Hilbert. Sém. Bourbaki (1959/60), no. 201.

    Google Scholar 

  17. LANG, S. Diophantine Geometry. (New York-London 1962).

    Google Scholar 

  18. ROBINSON, A. On ordered fields and definite functions. Math. Ann. 130 (1955), 257–271.

    Article  MathSciNet  MATH  Google Scholar 

  19. ROBINSON, A. On Hilbert's Irreducibility Theorem. Unpublished Manuscript.

    Google Scholar 

  20. ROBINSON, A. Nonstandard Analysis. (Amsterdam 1966)

    Google Scholar 

  21. ROBINSON, A.—ROQUETTE, P. On the Finiteness Theorem of Siegel and Mahler concerning Diophantine Equations. J. Number Theory 7 (1975), 121–176.

    Article  MathSciNet  MATH  Google Scholar 

  22. SCHINZEL, A. On Hilbert's Irreducibility theorem. Ann. Polon. Math. 16 (1965), 333–340

    MathSciNet  MATH  Google Scholar 

  23. SIEGEL, C.L. Über einige Anwendungen diophantischer Approximationen. Abh. Preuss. Akad. Wiss. Phys. Math. Kl. (1929), Nr. 1

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Daniel H. Saracino Volker B. Weispfenning

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag

About this paper

Cite this paper

Roquette, P. (1975). Nonstandard aspects of Hilbert's irreducibility theorem. In: Saracino, D.H., Weispfenning, V.B. (eds) Model Theory and Algebra. Lecture Notes in Mathematics, vol 498. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080983

Download citation

  • DOI: https://doi.org/10.1007/BFb0080983

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07538-7

  • Online ISBN: 978-3-540-38057-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics