Background:
Exercise 14:
Let $p$ be a fixed prime integer and let $R$ be the set of all rational numbers that can be written in the form $\frac{a}{b}$ with $b$ not divisible by $p. Prove that
(a) $R$ is an integral domain caontaining $\mathbb{Z}$. [Note $n=\frac{n}{1}$].
(b) If $\frac{a}{b}\in R$ and $p\nmid a$, then $\frac{a}{b}$ is a unit in $R.$
(c) If $I$ is a nonzero ideal in $R$ and $I\neq R$, then $I$ contains $p^t$ for some $t>0.$.
Questions:
I have a question about part (c) above. Specifically, If $R$ is defined as $R=\{\frac{a}{b}\in \mathbb{Q}\mid p\not\mid b, \text{ for some prime-}p \}$, then where does $p^t$ come from?