Situation 10.123.4 (00PW)—The Stacks project

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Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.123: Zariski's Main Theorem
Situation 10.123.4 (cite)

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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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