A Diophantine problem for Laurent polynomial rings

Pappas, Peter

doi:10.1090/S0002-9939-1985-0776209-6

A Diophantine problem for Laurent polynomial rings
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by Peter Pappas

Proc. Amer. Math. Soc. 93 (1985), 713-718

DOI: https://doi.org/10.1090/S0002-9939-1985-0776209-6

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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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