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.

  • $\begingroup$ Hints. The localization commutes with the quotients, and $3$ is invertible in $\mathbb Z_{(5)}$. $\endgroup$
    – user26857
    Apr 15 at 13:22
  • $\begingroup$ You might find this post helpful. $\endgroup$ Apr 15 at 14:55


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