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

MathSciNet review:
3105860

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Abstract: Let be a recursive ring whose quotient field is not algebraically closed with the property that Hilbert's Tenth Problem over is undecidable, and let be a non-empty proper subset of . We prove that it is not decidable whether the number of solutions of a diophantine equation with coefficients in is in .

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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:
https://doi.org/10.1090/S0002-9939-2013-11698-9

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