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.