On Generalized m-flat Modules

Let I be a right (left) ideal of a ring R. Then R/I is a right (left) generalized m flat modules (GmF module) if and only if for each , there exist and a fixed positive integer m such that . We study characterization and properties this class of flat modules, and we give the relation between this class and generalized m- flat modules and m regular rings, reduced rings, reversible rings and uniform rings.