Integral 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 an integral morphism if $$S$$ is an integral extension of the image of $$R$$ in $$S$$. Equivalently, we say that $$f$$ is an integral morphism if every element of $$S$$ satisfies a monic polynomial with coefficients in $$R$$.

Stronger properties

 * Finite morphism