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 étale 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.

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View Definition 15.104.1 as pdf