I am supposed to find a ring that is isomorphic to $\mathbb{Z}[1/3]/(5)$ using an isomorphism theorem. My guess is that $\mathbb{Z}[x]/(5,1+3x)$ is isomorphic to this and in turn I think that $\mathbb{F}_5[x]/(1+3x)$ is also isomorphic to this but I have no idea how to prove it other than I think I should use the isomorphism theorem if $S + I = R$, then $R/I \cong S/(S ∩ I)$.
2026-03-25 17:38:33.1774460313
Ring isomorphic to $\mathbb{Z}[1/3]/(5)$?
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