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Pseudo-algebraically closed rings

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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.

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Authors and Affiliations

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

    Luck Darnière

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  1. Luck Darnière
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Received: 29 March 1999 / Revised version: 4 July 2000

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Darnière, L. Pseudo-algebraically closed rings. manuscripta math. 105, 13–46 (2001). https://doi.org/10.1007/s002290170008

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  • DOI: https://doi.org/10.1007/s002290170008

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