# Integral morphism

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 $R$.