From reading Atiyah and MacDonald, I know of the result that a absolutely flat commutative ring has all principal ideals idempotent.
Reading around on math reference, I think that if a commutative ring $R$ is absolutely flat, (all $R$-modules are flat), then every ideal $H$ is idempotent, so $H^2=H$.
However, maybe my english is not so good, but I don't fully understand the proof provided there. I don't get the language "descend into tensor algebra and imagine..." and such. Is there a better polished proof of why all ideals in a absolutely flat ring $R$ are idempotent? Thank you very much.