Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 101 / 2 / a

A ring extension $A\subseteq B$ is an integral extension when every $b\in B$ is an integral element over $A$: there is a monic polynomialwith all $a_i\in A$.

A ring extension $A\subseteq B$ is finite when $B$ is a finitely generated module over $A$. Every finite extension is integral by the determinant trick.