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Decidability of Sub-theories of Polynomials over a Finite Field

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Mathematical Theory and Computational Practice (CiE 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5635))

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Abstract

Let \({\mathbb{F}}_q\) be a finite field with q elements. We produce an (effective) elimination of quantifiers for the structure of the set of polynomials, \({\mathbb{F}}_q[t]\), of one variable, in the language which contains symbols for addition, multiplication by t, inequalities of degrees, divisibility of degrees by a positive integer and, for each \(d\in{\mathbb{F}}_q[t]\), a symbol for divisibility by d. We discuss the possibility of extending our results to the structure which results if one includes a predicate for the relation “x is a power of t”.

Supported by the Trimester Program on Diophantine Equations, January - April 2009.

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Authors and Affiliations

  1. Hausdorff Research Institute for Mathematics, Poppelsdorfer Allee 45, D-53115, Bonn, Germany

    Alla Sirokofskich

  2. Department of Mathematics, University of Crete, 714 09, Heraklion, Greece

    Alla Sirokofskich

Authors
  1. Alla Sirokofskich
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Editors and Affiliations

  1. University of Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Klaus Ambos-Spies

  2. Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, Amsterdam, TV, The Netherlands

    Benedikt Löwe

  3. Institut für Informatik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Wolfgang Merkle

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Sirokofskich, A. (2009). Decidability of Sub-theories of Polynomials over a Finite Field. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds) Mathematical Theory and Computational Practice. CiE 2009. Lecture Notes in Computer Science, vol 5635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03073-4_45

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  • DOI: https://doi.org/10.1007/978-3-642-03073-4_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03072-7

  • Online ISBN: 978-3-642-03073-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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