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Ultraproducts and approximation in local rings. II

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References

  1. Artin, M.: On the solution of analytic equations. Invent. Math.5, 277–291 (1968)

    Google Scholar 

  2. Artin, M.: Algebraic approximation of structures over complete local rings. Publ. Math. I.H.E.S.36, 23–56 (1969)

    Google Scholar 

  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. 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. 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. Lang, S.: Algebra. Reading, MA: Addison-Wesley 1965

    Google Scholar 

  7. Pfister, G.: Einige Bemerkungen zur Struktur lokaler Henselscher Ringe. Beiträge Algebra Geometrie4, 47–51 (1975)

    Google Scholar 

  8. Pfister, G., Popescu, D.: Die strenge Approximationseigenschaft lokaler Ringe. Invent. Math.30, 145–174 (1975)

    Google Scholar 

  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. Tate, J.: Rigid analytic spaces. Invent. Math.12, 257–289 (1971)

    Google Scholar 

  11. Van der Put, M.: A Problem on coefficient fields and equations over local rings. Compositio Math.30, 235–258 (1975)

    Google Scholar 

  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. Zariski, O., Samuel, P.: Commutative algebra. I, II. Princeton: Van Nostrand 1960

    Google Scholar 

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Authors and Affiliations

  1. The Institute for Advanced Study, 08540, Princeton, NJ, USA

    J. Denef

  2. Purdue University, 47907, West Lafayette, IN, USA

    L. Lipshitz

Authors
  1. J. Denef
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  2. L. Lipshitz
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Additional information

The first author thanks the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek for its support. The authors would like to thank Princeton University and The Institute for Advanced Study, respectively, for their hospitality during part of the preparation of this paper

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Denef, J., Lipshitz, L. Ultraproducts and approximation in local rings. II. Math. Ann. 253, 1–28 (1980). https://doi.org/10.1007/BF01457817

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