## Tag `00HR`

Chapter 10: Commutative Algebra > Section 10.38: Flat modules and flat ring maps

Lemma 10.38.17. A flat local ring homomorphism of local rings is faithfully flat.

Proof.Immediate from Lemma 10.38.16. $\square$

The code snippet corresponding to this tag is a part of the file `algebra.tex` and is located in lines 8817–8820 (see updates for more information).

```
\begin{lemma}
\label{lemma-local-flat-ff}
A flat local ring homomorphism of local rings is faithfully flat.
\end{lemma}
\begin{proof}
Immediate from Lemma \ref{lemma-ff-rings}.
\end{proof}
```

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