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Hilbert's tenth problem for quadratic rings


Author: J. Denef
Journal: Proc. Amer. Math. Soc. 48 (1975), 214-220
MSC: Primary 10N05; Secondary 02F50, 10B99
DOI: https://doi.org/10.1090/S0002-9939-1975-0360513-3
MathSciNet review: 0360513
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Abstract: Let $ {\mathbf{A}}(D)$ be any quadratic ring; in this paper we prove that Hilbert's tenth problem for $ {\mathbf{A}}(D)$ is unsolvable, and we determine which relations are diophantine over $ {\mathbf{A}}(D)$.


References [Enhancements On Off] (What's this?)

  • [1] Z. I. Borevič and I. R. Šafarevič, Number theory, ``Nauka", Moscow, 1964; English transl., Pure and Appl. Math., vol. 20, Academic Press, New York, 1966. MR 30 #1080; 33 #4001. MR 0195803 (33:4001)
  • [2] Martin Davis, Hilbert's tenth problem is unsolvable, Amer. Math. Monthly, 80 (1973), 233-269. MR 0317916 (47:6465)
  • [3] Raphael M. Robinson, Undecidable rings, Trans. Amer. Math. Soc. 70 (1951), 137-159. MR 12, 791. MR 0041081 (12:791b)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0360513-3
Keywords: Hilbert's tenth problem, unsolvable problems, diophantine equations, recursive functions
Article copyright: © Copyright 1975 American Mathematical Society

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