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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
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)$.


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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