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 .

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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