1.6.12 Fields, Groups, Rings

Problem: Is \( \left\{\left.\frac{m}{n} \right\rvert\, m, n \in \mathbb{Z} ; n \notin p \mathbb{Z} ; m \in p \mathbb{Z}\right\} \) ideal in the \( \mathbb{Q}_{p} \), ring of all rational numbers, represented in the form of a fraction with a denominator not divided into a simple number \( p \) ?