Situation 10.123.4. Let $R$ be a ring. Let $\varphi : R[x] \to S$ be finite. Let

\[ J = \{ g \in S \mid gS \subset \mathop{\mathrm{Im}}(\varphi )\} \]

be the “conductor ideal” of $\varphi $. Assume $\varphi (R) \subset S$ integrally closed in $S$.

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