7 at 0:34 Math Gems 1,679 5 feedback up vote 2 down vote As an alternative approach, what you're really doing here is taking a localization of $\mathbb{Z}$. In fact, if we let $$S=\{\pm 1\}\cup \{\pm p_1p_2 \cdots p_n\,\vert\,p_i \textrm{ is an odd prime }\}$$ then $R=\mathbb{Z}_S=\{\frac{a}{b}\,\vert\,a\in \mathbb{Z}, b\in S\}$ is