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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A Diophantine problem for Laurent polynomial rings

Author: Peter Pappas
Journal: Proc. Amer. Math. Soc. 93 (1985), 713-718
MSC: Primary 03D35; Secondary 11U05
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}}]$.

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PII: S 0002-9939(1985)0776209-6
Keywords: Diophantine problems, unsolvable problems, Hilbert's tenth problem
Article copyright: © Copyright 1985 American Mathematical Society