Local to Global

Let R be an integral domain of finite type over \mathbb{Z}, whose quotient field is of characteristic zero. Let \alpha\in R be an element such that at every closed point \mathfrak{p} the image of \alpha in the residue field R/\mathfrak{p} lies in the prime field \mathbb{F}_p (where p = \mathfrak{p}\cap\mathbb{Z}). Prove that \alpha must be in \mathbb{Q}.

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Local to Global

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