Diophantine definability over some rings of algebraic numbers with infinite number of primes allowed in the denominator |
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| Authors: | Alexandra Shlapentokh |
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| Affiliation: | (1) Department of Mathematics, East Carolina University, Greenville, NC 27858, USA (e-mail: mashlape@ecuvax.cis.ecu.edu), US |
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| Abstract: | Let K be a number field. Let W be a set of non-archimedean primes of K, let O K , W ={x∈K∣ord p x≥0∀p∉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 , W . (Thus, the Diophantine problem of O K , W is undecidable.) Oblatum 25-III-1996 & 31-X-1996 |
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