Mathematische Annalen

, Volume 253, Issue 1, pp 1–28 | Cite as

Ultraproducts and approximation in local rings. II

  • J. Denef
  • L. Lipshitz


Local Ring 
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  1. 1.
    Artin, M.: On the solution of analytic equations. Invent. Math.5, 277–291 (1968)Google Scholar
  2. 2.
    Artin, M.: Algebraic approximation of structures over complete local rings. Publ. Math. I.H.E.S.36, 23–56 (1969)Google Scholar
  3. 3.
    Becker, J., Denef, J., Lipshitz, L., van den Dries, L.: Ultraproducts and approximation in local rings. I. Invent. Math.51, 189–203 (1979)Google Scholar
  4. 4.
    Gabriélov, A.M.: Formal relations between analytic functions. Funkcional. Anal. i. Priložen.5, 64–65 (1971); Functional Anal. Appl.5, 318–319 (1971)Google Scholar
  5. 5.
    Kurke, H., Pfister, G., Popescu, D., Roczen, M., Mostowski, T.: Die Approximationseigenschaft lokaler Ringe. Lecture Notes in Mathematics, No. 634. Berlin, Heidelberg, New York: Springer 1978 [Zbl.401, 13013 (1979)]Google Scholar
  6. 6.
    Lang, S.: Algebra. Reading, MA: Addison-Wesley 1965Google Scholar
  7. 7.
    Pfister, G.: Einige Bemerkungen zur Struktur lokaler Henselscher Ringe. Beiträge Algebra Geometrie4, 47–51 (1975)Google Scholar
  8. 8.
    Pfister, G., Popescu, D.: Die strenge Approximationseigenschaft lokaler Ringe. Invent. Math.30, 145–174 (1975)Google Scholar
  9. 9.
    Siu, Yum-Tong: Noetherianness of rings of holomorphic functions on Stein compact subsets. Proc. Am. Math. Soc.21, 483–489 (1969)Google Scholar
  10. 10.
    Tate, J.: Rigid analytic spaces. Invent. Math.12, 257–289 (1971)Google Scholar
  11. 11.
    Van der Put, M.: A Problem on coefficient fields and equations over local rings. Compositio Math.30, 235–258 (1975)Google Scholar
  12. 12.
    Wavrik, J.J.: A theorem on solutions of analytic equations with applications to deformations of complex structures. Math. Ann.216, 127–142 (1975)Google Scholar
  13. 13.
    Zariski, O., Samuel, P.: Commutative algebra. I, II. Princeton: Van Nostrand 1960Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • J. Denef
    • 1
  • L. Lipshitz
    • 2
  1. 1.The Institute for Advanced StudyPrincetonUSA
  2. 2.Purdue UniversityWest LafayetteUSA

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