Diophantine definability over some rings of algebraic numbers with infinite number of primes allowed in the denominator

• 成果类型: Article
• 署名作者: Shlapentokh, A
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220050170
• 发表日期: 1997
• 页码: 489-507
• 关键词: hilbert 10th problem; function-fields; holomorphy rings; finite-fields; undecidability; unsolvability; constants; Integers

摘要

Let K be a number field. Let W be a set of non-archimedean primes of K, let O-K,O-W = (x is an element of K \ ord(p)x greater than or equal to 0 For All p is an element of W). Then if K is a totally real non-trivial cyclic extension of Q, there exists an infinite set W of finite primes of K such that Z and the ring of algebraic integers of K have a Diophantine definition over O-K,O-W (Thus, the Diophantine problem of O-K,O-W is undecidable.).