# flat module

A right module $M$ over a ring $R$ is flat if the tensor product functor $M\otimes_{R}(-)$ is an exact functor.

Similarly, a left module $N$ over $R$ is flat if the tensor product functor $(-)\otimes_{R}N$ is an exact functor.

Title flat module FlatModule 2013-03-22 12:09:45 2013-03-22 12:09:45 antizeus (11) antizeus (11) 6 antizeus (11) Definition msc 16D40 flat