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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Diophantine sets over polynomial rings
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by Karim Zahidi PDF
Proc. Amer. Math. Soc. 128 (2000), 877-884 Request permission

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 $R[t]$.
References
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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
  • 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.
  • © Copyright 1999 American Mathematical Society
  • 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
  • MathSciNet review: 1641141