On Diophantine sets over polynomial rings

We prove that the recursively enumerable relations over a polynomial ring R[t], where R is the ring of integers in a totally real number field, are exactly the Diophantine relations over R[t].

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2000-03, Vol.128 (3), p.877-884
Main Author: Zahidi, Karim
Format: Article
Language:English
Subjects:
Algebra
Coefficients
Diophantine sets
Integers
Mathematical constants
Mathematical rings
Natural numbers
Numbers
Polynomials
Real numbers
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Description
Summary:We prove that the recursively enumerable relations over a polynomial ring R[t], where R is the ring of integers in a totally real number field, are exactly the Diophantine relations over R[t].
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-99-05179-5