Finitely generated morphism

This article defines a property that can be evaluated for a homomorphism of commutative unital rings

Definition

Suppose $R$ and $S$ are commutative unital rings and $f:R\to S$ is a homomorphism of commutative unital rings. Then, we say that $f$ is a finitely generated morphism if $S$ is finitely generated as an $R$-algebra; in other words, there exists a finite subset of $S$, that, along with the image $f(R)$, generates $S$.

Relation with other properties

Stronger properties

• Finite morphism