Finite Morphisms

Definition: A morphism of rings $\varphi \colon A \longrightarrow B$ is called finite, if $B$ is finitely generated as an -module, that is, there is an epimorphism of -modules

$A^{\oplus n} \twoheadrightarrow B$

for some $n \in \mathbb{N}$.

Fact: Finite morphisms are affine.

[latexpackage]