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Let $R=\mathbb{Z}[a_1,\ldots,a_n]$ be an integral domain finitely generated over $\mathbb{Z}$. Can the quotient group $(R,+)/(\mathbb{Z},+)$ contain a divisible element? By a "divisible element" I mean an element $e\ne 0$ such that for every positive integer $n$ there is an element f such that $e=nf$.

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    Do you mean $R$ modulo the image of $\mathbb{Z}$, or do you want to assume that $\mathbb{Z}$ injects into $R$, i.e., that $R$ has characteristic zero?2012-04-07

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