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 $e=nf$.

Note: I am not assuming that the $a_i$ are algebraically independent. 

Note: I previously posted this to Math StackExchange here: http://math.stackexchange.com/questions/71031/a-question-about-the-additive-group-of-a-finitely-generated-integral-domain