Flatness
From the definition, one can see that localization of modules is an exact functor, or in other words (reading this in the tensor product) that S−1R is a flat module over R. This is actually foundational for the use of flatness in algebraic geometry, saying in particular that the inclusion of an open set in Spec(R) (see spectrum of a ring) is a flat morphism.
Read more about this topic: Localization Of A Module
Famous quotes containing the word flatness:
“On a level plain, simple mounds look like hills; and the insipid flatness of our present bourgeoisie is to be measured by the altitude of its “great intellects.””
—Karl Marx (1818–1883)