The Stacks project

Definition 15.104.1. A ring $A$ is called absolutely flat if every $A$-module is flat over $A$. A ring map $A \to B$ is weakly ├ętale or absolutely flat if both $A \to B$ and $B \otimes _ A B \to B$ are flat.

Comments (4)

Comment #1194 by Max on

Evidently the arrow should go the other way round.

Comment #1207 by on

Whoops! Very silly indeed. Thanks for pointing this out. Fixed here.

Comment #1657 by on

It might be relevant to know that absolutely flat rings are also called von Neumann regular.

Comment #1673 by on

OK, I pointed this out in the text following the definition. See here.

Post a comment

Your email address will not be published.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.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 092B. Beware of the difference between the letter 'O' and the digit '0'.