2021
DOI: 10.48550/arxiv.2107.11266
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Decidability of the theory of addition and the Frobenius map in rings of rational functions

Abstract: We prove model completeness for the theory of addition and the Frobenius map for certain subrings of rational functions in positive characteristic. More precisely: Let p be a prime number, F p the prime field with p elements, F a field algebraic over F p and z a variable. We show that the structures of rings R, which are generated over F [z] by adjoining a finite set of inverses of irreducible polynomials of F [z] (e.g., R = F p [z, 1 z ]), with addition, the Frobenius map x → x p and the predicate '∈ F ' -tog… Show more

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