Abstract: By introducing the ∞copure flat modules, we proved that R is a QF ring if and only if R is left Noetherian ring and every finitely presented left Rmodule is ∞copure flat; R is a right IF ring if and only if every left Rmodule is ∞copure flat; R is a left CFH ring if and only if ∞copure flat modules are closed to their submodules; a left coherent ring R is a semihereditary ring if and only if ∞copure flat left Rmodules are flat.

Key words: ∞copure flat module, IF ring, semihereditary ring, CFH ring, QF ring