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Proceedings of the American Mathematical Society

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On Diophantine sets over polynomial rings


Author: Karim Zahidi
Journal: Proc. Amer. Math. Soc. 128 (2000), 877-884
MSC (1991): Primary 03D20; Secondary 11U05, 12L05
DOI: https://doi.org/10.1090/S0002-9939-99-05179-5
Published electronically: July 6, 1999
MathSciNet review: 1641141
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Abstract: 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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Additional Information

Karim Zahidi
Affiliation: Universiteit Gent, Vakgroep Kwantitatieve Technieken, Hoveniersberg 4, B-9000 Gent, Belgium
Address at time of publication: Department of Applied Mathematics and Computer Science, Krijgslaan 281, sg, B-9000 Gent, Belgium
Email: Karim.Zahidi@rug.ac.be

DOI: https://doi.org/10.1090/S0002-9939-99-05179-5
Received by editor(s): September 16, 1997
Received by editor(s) in revised form: April 22, 1998
Published electronically: July 6, 1999
Additional Notes: The author would like to thank Professor J. Van Geel for his help during the preparation of this work.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 1999 American Mathematical Society