# Integral morphism

From Commalg

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

## Definition

Suppose and are commutative unital rings and is a homomorphism of commutative unital rings. Then, we say that is an *integral morphism* if is an integral extension of the image of in . Equivalently, we say that is an integral morphism if every element of satisfies a monic polynomial with coefficients in .