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Elimination theory for addition and the frobenius map in polynomial rings

Published online by Cambridge University Press:  12 March 2014

Thanases Pheidas  and
Karim Zahidi
Thanases Pheidas
Affiliation:
Department of Mathematics, University of Crete, P.O. Box 2208, Heraklion. Crete, Greece, E-mail: [email protected]
Karim Zahidi
Affiliation:
Equipe de Logique Mathématique, UFR de Mathématiques (Case 7012), Université Denis-Diderot PARIS 7.2 Place Jussieu, 75251 Paris Cedex 05, France, E-mail: [email protected]
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Abstract.

We develop an elimination theory for addition and the Frobenius map over rings of polynomials. As a consequence we show that if F is a countable, recursive and perfect field of positive characteristic p, with decidable theory, then the structure of addition, the Frobenius map x → xp and the property ‘x ∈ F1, over the ring of polynomials F[T], has a decidable theory.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 4 , December 2004 , pp. 1006 - 1026
Copyright
Copyright © Association for Symbolic Logic 2004

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References

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