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I'm studying some results about flatness and faithful flatness and I'd like to keep in my mind some examples about faithfully flat modules.

In general, free modules are the typical examples.
Another (unusual) example of faithfully flat module is the "Zariski Covering". (Let $R$ be a ring, $(f_1,\dots,f_n)=R$, and let $R_{f_i}$ be a localization $\forall i$. Then $S:=\bigoplus_{i=1}^n R_{f_i}$ is called Zariski covering.)

Do you have any other example?

  • 8
    Your definition of Zariski covering is missing the important condition that the $f_i$ generate the unit ideal. Regards,2011-05-27
  • 1
    Indeed, if the $f_i$ do not generate the unit ideal, there exists a maximal ideal $m$ containing all the $f_i$. In this case, the extension of $m$ to $S$ is all of $S$ and $S$ cannot be a faithfully flat $R$-module.2011-06-01

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