Proposition 10.138.13. Let $R \to S$ be a ring map. The following are equivalent

$R \to S$ is of finite presentation and formally smooth,

$R \to S$ is smooth.

Proposition 10.138.13. Let $R \to S$ be a ring map. The following are equivalent

$R \to S$ is of finite presentation and formally smooth,

$R \to S$ is smooth.

**Proof.**
Follows from Proposition 10.138.8 and Definition 10.137.1. (Note that $\Omega _{S/R}$ is a finitely presented $S$-module if $R \to S$ is of finite presentation, see Lemma 10.131.15.)
$\square$

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like `$\pi$`

). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (0)

There are also: