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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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The number of solutions of a diophantine equation over a recursive ring
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by Christoph Baxa PDF
Proc. Amer. Math. Soc. 141 (2013), 4175-4178 Request permission

Abstract:

Let $R$ be a recursive ring whose quotient field is not algebraically closed with the property that Hilbert’s Tenth Problem over $R$ is undecidable, and let $A$ be a non-empty proper subset of $\{0,1,2,\ldots \}\cup \{\aleph _0\}$. We prove that it is not decidable whether the number of solutions of a diophantine equation with coefficients in $R$ is in $A$.
References
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Additional Information
  • Christoph Baxa
  • Affiliation: Department of Mathematics, University of Vienna, Nordbergstraße 15, A–1090 Wien, Austria
  • Email: christoph.baxa@univie.ac.at
  • Received by editor(s): December 1, 2011
  • Received by editor(s) in revised form: February 12, 2012
  • Published electronically: August 20, 2013
  • Communicated by: Julia Knight
  • © Copyright 2013 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 4175-4178
  • MSC (2010): Primary 11U05; Secondary 03B25, 11D45
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11698-9
  • MathSciNet review: 3105860