IFP-Flat Modules And IFP-Injective Modules Relative To The W-Operation

In this thesis,we mainly study the analogues of IFP-flat modules and IFPinjective modules in terms of w-module theory over commutative rings.Firstly,we study the w-module theoretic analogue of IFP-flat modules and IFP-injective modules.The concepts of w-IFP-flat modules and w-IFP-injective modules are introduced,their basic properties are discussed,and their equivalent characterizations are given.In addition,we also discussed w-PFP rings(i.e.,commutative rings in which every finitely presented ideal is w-split).Some characterizations of w-PFP rings are given.It is shown that a commutative ring R is a wPFP ring if and only if every quotient module of a w-IFP-injective R-module is w-IFPinjective,if and only if every submodule of w-IFP-flat R-module is w-IFP-flat.Secondly,a proper subclass of the IFP-flat modules and that of IF P-injective modules,called GV-IFPflat modules and GV-IFP-injective modules respectively,are investigated,and some of their basic properties are discussed.Moreover,GV-coherent rings are also introduced,and some equivalent characterizations of GV-coherent rings are given by using GV-IFP-flat modules and GV-IFP-injective modules.It is proved that a commutative ring R is GV-coherent if and only if every direct product of GV-IFP-flat R-module is GV-IFP-flat,if and only if every direct limit of GV-IFP-injective R-module is GV-IFP-injective.