DIOPHANTINE SETS OF POLYNOMIALS OVER NUMBER FIELDS

被引：4

作者：

Demeyer, Jeroen ^{[1
]}

机构：

[1] Univ Ghent, Dept Math, B-9000 Ghent, Belgium

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2010年 / 138卷 / 08期

关键词：

Diophantine set; recursively enumerable set; Hilbert's tenth problem; RECURSIVELY-ENUMERABLE SETS; HILBERTS 10TH PROBLEM; P-ADIC FIELDS; FINITE-FIELD; RINGS;

D O I：

10.1090/S0002-9939-10-10329-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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[7]. Applying a result by Denef, this implies that every recursively enumerable subset of R[T](k) is diophantine over R[T].

引用

页码：2715 / 2728

页数：14

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