The diophantine problem for addition and divisibility for subrings of rational functions over finite fields
Keywords:Positive-existential definability, Finite field of odd characteristic
It is shown that the positive existential theory of the structure ℱS = (S−1F[t];=,F, 0, 1,+, |, f ↦ tf), where f ↦ tf is the multiplication by t map, S is non-empty a finite set of irreducible polynomials, and F is a finite field of odd characteristic, is undecidable.
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