Some Modules Under Faithfully Flat Ring Extensions

This paper mainly focuses on some modules under faithful flat ring extensions.The first chapter contains some preparation knowledge.In the second chapter,we main-ly study(?)-Gorenstein injective modules,whereis a class consisting of all injective-modules with finite flat dimensions,and(?)is a class consisting of all injective-modules with finite flat dimensions.Letbe a commutative ring andbe a faithfully flat-algebra.It is proved,under some extra assumptions,that an-moduleis(?)-Gorenstein injective module if and only ifis strongly cotorsion and Hom_R(S,N)is a(?)-Gorenstein injective-module.In the third chapter,we mainly study weak Gorenstein injective modules under faithful flat ring extensions.Chapter 4 focuses on restricted in-jective modules under faithful flat ring extensions.