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I need some help to find faithfully flat abelian groups.

Flat abelian groups are torsion free $\mathbb{Z}$-modules. But what about faithfully flat abelian groups. $\mathbb{Q}$ is an example that is torsionfree (flat) but not faithfully flat $\mathbb{Z}$-module.

How do we describe all faithfully flat abelian groups?

Thanks for your help...

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A $\mathbb Z$-module $M$ is faithfully flat iff it is torsion free and $pM\ne M$ for any prime number $p$.

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  • $\begingroup$ I just realize that it is not so hard to think because of Q_Z. But i couldn't. Thanks again. $\endgroup$
    – etk
    Commented Mar 9, 2015 at 8:25

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