Diophantine sets over $\textbf {Z}[T]$
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- by J. Denef PDF
- Proc. Amer. Math. Soc. 69 (1978), 148-150 Request permission
Abstract:
Let ${\mathbf {Z}}[T]$ be the ring of polynomials with integer coefficients. We prove that every recursively enumerable subset of ${\mathbf {Z}}[T]$ is diophantine over ${\mathbf {Z}}[T]$. This extends a theorem of Davis and Putnam which states that every recursively enumerable subset of Z is diophantine over ${\mathbf {Z}}[T]$.References
- Martin Davis, Hilbert’s tenth problem is unsolvable, Amer. Math. Monthly 80 (1973), 233–269. MR 317916, DOI 10.2307/2318447
- Martin Davis and Hilary Putnam, Diophantine sets over polynomial rings, Illinois J. Math. 7 (1963), 251–256. MR 147387
- Y. Pourchet, Sur la représentation en somme de carrés des polynômes à une indéterminée sur un corps de nombres algébriques, Acta Arith. 19 (1971), 89–104 (French). MR 289442, DOI 10.4064/aa-19-1-89-104
- Michael O. Rabin, Computable algebra, general theory and theory of computable fields, Trans. Amer. Math. Soc. 95 (1960), 341–360. MR 113807, DOI 10.1090/S0002-9947-1960-0113807-4
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 69 (1978), 148-150
- MSC: Primary 02F50; Secondary 10B99, 10N99
- DOI: https://doi.org/10.1090/S0002-9939-1978-0462934-X
- MathSciNet review: 0462934