Finite morphism

{curing-homomorphism property}}

Definition

Suppose $R$ and $S$ are commutative unital rings and $f:R\to S$ is a homomorphism of commutative unital rings. This makes $S$ naturally into a $R$-module. Then, $f$ is termed finite if $S$ is a finitely generated module over $R$.

When the morphism is injective, we say that $S$ is a finite extension of $R$.