faithfully flat

Let A be a commutative ring. Then M if faithfully flat if for any A-modules P,Q, and R, we have


is exact if and only if the M-tensored sequence


is exact. (Note that the “if and only if” clause makes this stronger than the definition of flatness).

Equivalently, an A-module M is faithfully flat iff M is flat and the functorMathworldPlanetmath -AM is a faithful functorMathworldPlanetmath (and hence the name).

Title faithfully flat
Canonical name FaithfullyFlat
Date of creation 2013-03-22 14:35:55
Last modified on 2013-03-22 14:35:55
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 5
Author mathcam (2727)
Entry type Definition
Classification msc 16D40