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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 $ R$ be an integral domain of characteristic zero. We prove that the diophantine problem for the Laurent polynomial ring $ R[T,{T^{ - 1}}]$ with coefficients in $ {\mathbf{Z}}[T]$ is unsolvable. Under suitable conditions on $ R$ we then show that either $ {\mathbf{Z}}$ or $ {\mathbf{Z}}[i]$ is diophantine over $ R[T,{T^{ - 1}}]$.


References [Enhancements On Off] (What's this?)

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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

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