  In this article first we develop the Gabriel localizations (abbreviated as
G-localizations) for commutative rings, specially some new results in this
direction are proven. Then, as an application, it is shown that a ring map is a
flat epimorphism if and only if it corresponds to a kind of the
G-localizations. As a by-product of this study, a characterization for the
flatness of the quotient rings is given. The exactness of the G-localization
functor are characterized. The structure of prime ideals in the G-localization
rings are also studied. Finally, it is shown that the Gabriel localization
theory is a natural generalization of the usual localization theory.
