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manuscripta mathematica

, Volume 105, Issue 1, pp 13–46 | Cite as

Pseudo-algebraically closed rings

  • Luck Darnière

Abstract:

We use a variant of the nonsingular Hasse Principle to define a class of rings analogeous to PAC fields, and prove that this class has nice model theoretical properties. Since there are a lot of examples of such rings which are of interest for arithmetical purpose we apply our study to those examples, obtaining several decidability results and one purely algebraic application.

Mathematics Subject Classification (2000): 12L05, 12L12, 13L05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Luck Darnière
    • 1
  1. 1.Université d'Angers, 2 Bd Lavoisier, 49045 Angers Cedex 01, France.¶e-mail: Luck.Darniere@univ-angers.frFR

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