Diophantine Sets of Polynomials over Number Fields
نویسنده
چکیده
Let R be a number field or a recursive subring of a number field and consider the polynomial ring R[T ]. We show that the set of polynomials with integer coefficients is diophantine over R[T ]. Applying a result by Denef, this implies that every recursively enumerable subset of R[T ]k is diophantine over R[T ].
منابع مشابه
Diophantine sets of polynomials over finitely generated fields in characteristic zero
Let R be a recursive noetherian integral domain of characteristic zero with fraction field K. Assume that K is finitely generated (as a field) over Q. Equivalently, assume that K is the function field of a variety over a number field. We show that recursively enumerable sets are diophantine for the polynomial ring R[Z]. 2000 MSC: 11D99 (primary), 03D25, 12L12, 11R58, 12E10 (secondary).
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