Definition 15.104.1 (092B)—The Stacks project

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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 December 06, 2014 at 20:20

Evidently the arrow $B \to B \otimes_A B$ should go the other way round.

Comment #1207 by Johan on December 08, 2014 at 14:26

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

Comment #1657 by Pieter Belmans on September 28, 2015 at 08:25

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

Comment #1673 by Johan on October 08, 2015 at 16:57

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

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