Integral extension

Definition

Let $R \le S$ be commutative unital rings. We say that $S$ is an integral extension of $R$ if, for any element $a \in S$, there exists a monic polynomial $p(x) \in R[x]$ such that $p(a) = 0$.

Note that any integral extension is algebraic.

Metaproperties

Any integral extension of an integral extension is an integral extension.