A Diophantine problem for Laurent polynomial rings
Author:
Peter Pappas
Journal:
Proc. Amer. Math. Soc. 93 (1985), 713-718
MSC:
Primary 03D35; Secondary 11U05
DOI:
https://doi.org/10.1090/S0002-9939-1985-0776209-6
MathSciNet review:
776209
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Abstract: Let be an integral domain of characteristic zero. We prove that the diophantine problem for the Laurent polynomial ring
with coefficients in
is unsolvable. Under suitable conditions on
we then show that either
or
is diophantine over
.
- [1] M. Davis, Hilbert's tenth problem is unsolvable, Amer. Math. Monthly 80 (1973), 233-269. MR 0317916 (47:6465)
- [2] J. Denef, Hilbert's tenth problem for quadratic rings. Proc. Amer. Math. Soc. 48 (1975), 214-220. MR 0360513 (50:12961)
- [3] -, The diophantine problem for polynomial rings and fields of rational functions, Trans. Amer. Math. Soc. 242 (1978), 391-399. MR 0491583 (58:10809)
- [4] -, Diophantine sets over algebraic integer rings. II, Trans. Amer. Math. Soc. 257 (1980), 227-236. MR 549163 (81b:12031)
- [5] M. O. Rabin, Computable algebra, general theory and theory of computable fields, Trans. Amer. Math. Soc. 95 (1960), 341-360. MR 0113807 (22:4639)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1985-0776209-6
Keywords:
Diophantine problems,
unsolvable problems,
Hilbert's tenth problem
Article copyright:
© Copyright 1985
American Mathematical Society