Finitely generated morphism

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 $$S$$.

Stronger properties

 * Finite morphism