Faithfully Flat Module

A module over a unit ring is called faithfully flat if the tensor product functor is exact and faithful.

A faithfully flat module is always flat and faithful, but the converse does not hold in general. For example, is a faithful and flat -module, but it is not faithfully flat: in fact reduces all the quotient modules (and the maps between them) to zero, since for all and all :

See also

Faithful functor, Faithful Module, Flat Module

This entry contributed by Margherita Barile

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References

Lam, T. Y. "Flat and Faithfully Flat Modules." §4 in Lectures on Modules and Rings. New York: Springer-Verlag, pp. 122-164, 1999.

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Faithfully Flat Module

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Barile, Margherita. "Faithfully Flat Module." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/FaithfullyFlatModule.html

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