Lemma 10.6.2. The notions finite type and finite presentation have the following permanence properties.
A composition of ring maps of finite type is of finite type.
A composition of ring maps of finite presentation is of finite presentation.
Given R \to S' \to S with R \to S of finite type, then S' \to S is of finite type.
Given R \to S' \to S, with R \to S of finite presentation, and R \to S' of finite type, then S' \to S is of finite presentation.
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