On CT-injective Modules And FGT-rings

The injective rings play an important role in the study of rings and categories of modules . First , we introduce the notion of ann-injective rings and CT-injective modules .Second,we make an inquiry into a series of their properties.Third,we give the definition of homological dimension of CT-injective modules.At last,we give the definition of FGT rings which is the extension of cogenerator rings.We study the relation of FGT rings and CT-injective rings and its some properties.In §1,We give the definition of ann-injective rings and some equivalent conditions.In §2,the definition of FGT-injective modules impire us to introduce the definition of CT-injective modules.In this chapter,we discover that ann-injective rings are just CT-injective rings.They are studies from that two different facts.The ann-injective rings start at the angle of annihilator,at the same time,the CT-injective rings start at the angle of cycle tortionless modules.In §3,we introduce the definition of homological dimension of CT-injective modules that make us further know CT-injective modules from angle of dimension.In §4,we give the definition of FGT rings which is the extension of cogenerator rings.We get some properties and the relation of it and CT-injective rings.