# The Stacks Project

## Tag 02JM

Lemma 10.35.15. Let $A \to B \to C$ be ring maps.

1. If $A \to C$ is integral so is $B \to C$.
2. If $A \to C$ is finite so is $B \to C$.

Proof. Omitted. $\square$

The code snippet corresponding to this tag is a part of the file algebra.tex and is located in lines 7356–7363 (see updates for more information).

\begin{lemma}
\label{lemma-integral-permanence}
Let $A \to B \to C$ be ring maps.
\begin{enumerate}
\item If $A \to C$ is integral so is $B \to C$.
\item If $A \to C$ is finite so is $B \to C$.
\end{enumerate}
\end{lemma}

\begin{proof}
Omitted.
\end{proof}

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