Hilbert’s tenth problem for quadratic rings
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- by J. Denef PDF
- Proc. Amer. Math. Soc. 48 (1975), 214-220 Request permission
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
- A. I. Borevich and I. R. Shafarevich, Number theory, Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. Translated from the Russian by Newcomb Greenleaf. MR 0195803
- Martin Davis, Hilbert’s tenth problem is unsolvable, Amer. Math. Monthly 80 (1973), 233–269. MR 317916, DOI 10.2307/2318447
- Raphael M. Robinson, Undecidable rings, Trans. Amer. Math. Soc. 70 (1951), 137–159. MR 41081, DOI 10.1090/S0002-9947-1951-0041081-0
Additional Information
- © Copyright 1975 American Mathematical Society
- 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