Hilbert’s Tenth Problem over Function Fields of Positive Characteristic Not Containing the Algebraic Closure of a Finite Field
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چکیده
We prove that the existential theory of any function field K of characteristic p > 0 is undecidable in the language of rings provided that the constant field does not contain the algebraic closure of a finite field. We also extend the undecidability proof for function fields of higher transcendence degree to characteristic 2 and show that the first-order theory of any function field of positive characteristic is undecidable in the language of rings without parameters.
منابع مشابه
Hilbert’s Tenth Problem for Algebraic Function Fields of Characteristic 2
Let K be an algebraic function field of characteristic 2 with constant field CK . Let C be the algebraic closure of a finite field in K. Assume that C has an extension of degree 2. Assume that there are elements u, x of K with u transcendental over CK and x algebraic over C(u) and such that K = CK(u, x). Then Hilbert’s Tenth Problem over K is undecidable. Together with Shlapentokh’s result for ...
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