The question asks to prove the set $R$ is an integral domain, where $R$ is defined as $\{\frac{a}{b}: a,b\in\Bbb Z, b\in 2\Bbb Z+1\}$.
I know that a set is an integral domain when there exists no zero devisors in that set. I also know that a zero devisor exists when there exists two non-zero elements in a set that when multiplied together equal $0$. Is its okay when answering this question to say that it is simply impossible for $a/b$ to equal $0$ unless the integer $a$ is equal to $0$, and therefore no zero devisors exist?
Thank you.