Is $\mathbb{C}$ a faithfully flat $\mathbb{R}$-module? In the general case, is it true that if $k$ is a field and $K$ is it's algebraic closure then $K$ is a faithfully flat $k$-module?
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2026-04-25 08:49:48.1777106988
Are field extensions faithfully flat?
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All extensions of fields are faithfully flat.
You can use the criterion that every prime ideal of the small field is the inverse image of one in the large field.