# Describe the localization

I recently got a rather vague question which stated

Describe the localization $$(\mathbb{Z} / 15\mathbb{Z})_{(5)}$$ (away from the prime ideal $$(5)$$).

I know now that this localization is somehow isomorphic to the ring $$\mathbb{Z} / 5\mathbb{Z}$$, but I am not sure how to prove it. Any help would be appreciated.

• Hints. The localization commutes with the quotients, and $3$ is invertible in $\mathbb Z_{(5)}$. Apr 15 at 13:22
• You might find this post helpful. Apr 15 at 14:55