In this paper,by weakening the ideal condition of the flat module to finitely-presented annihilator ideal condition,the notion of FPA-flat module is defined,its equivalent definitions and properties are studied.

This article from viewpoint of dimension obtained an equal characterization of injective module and flat module with better duality.

Gives　a　definition　of　Lflat　modules　and　some　properties　of　them,　then　discusses　some　equivalent　relations　of　Linjective　modules,　Lprojective　modules,　Lflat　modules,L(semi)hereditary　modules　(rings)　under　almost　excellent　extensions.

The properties of injective and flat modules over Noetherian ring are discussed.

Using coflat modules and M-semi-hereditary rings, it is obtained that R is a semi- hereditary ring iff the factors of E(R) is coflat iff R is a R-semi-hereditary ring iff the sum of two injective submodules in a module that are isomorphic is coflat.

The concept of coflat on LLU Rings are given,some results are obtained about homology,and the results between FP-injective module and coflat module are give

R is sufficient condition of IF rings,where R is coherent rings and R_R and ()_RR is coflat module.

This article mainly uses fpn-flat left R-modules to investigate the existences of relative preenvelopes of left R-modules.