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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The number of solutions of a diophantine equation over a recursive ring


Author: Christoph Baxa
Journal: Proc. Amer. Math. Soc. 141 (2013), 4175-4178
MSC (2010): Primary 11U05; Secondary 03B25, 11D45
Published electronically: August 20, 2013
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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$.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11698-9
PII: S 0002-9939(2013)11698-9
Keywords: Hilbert's Tenth Problem, recursive ring
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
Article copyright: © Copyright 2013 American Mathematical Society