Let $\mathbb{Z}_{(p)} = \left\{\frac{a}{b}\in\mathbb{Q}:p\nmid b\right\}$
How is it posible to show that $\mathbb{Z}_{(p)}/p\mathbb{Z}_{(p)}$ is ismorphic to $\mathbb{Z}/p\mathbb{Z}$.
I want to show there is sujective homomorphism $\mathbb{Z}_{(p)}/p\mathbb{Z}_{(p)}$ to $\mathbb{Z}/p\mathbb{Z}$. But I'm unable to get the correct map.