Artin--Tate lemma
= Artin--Tate lemma
{c}
{wiki}
Let $A\subseteq B\subseteq C$ be rings. If $A$ is Noetherian, $C$ is a finitely generated $A$-algebra, and $C$ is a finite $B$-module, then $B$ is a finitely generated $A$-algebra.
= Artin--Tate lemma
{c}
{wiki}
Let $A\subseteq B\subseteq C$ be rings. If $A$ is Noetherian, $C$ is a finitely generated $A$-algebra, and $C$ is a finite $B$-module, then $B$ is a finitely generated $A$-algebra.