SP-algebra And C-flat Mode

In this thesis, we investigate some parts as follows:In the first part, we introduce notions of IG-injective modules base on G-injevtive modules and SG-injevtive modules, and also used the properties of irreducible morphism. We mainly discuss some charac-terizations of IG-injective module and then we prove a conclusion, which is if a simple module is SG-injective module, then it is a injev-tive modules or there exist an irreducible morphism from a injevtive modules to itself. Further, we prove a strongly conclusion, the mod-ules of ring R are direct sum of simple modules and injevtive modules.In the second part, we introduce the form of the algebra which its modules modR=S(R)(?) P(R) based on IG-injevtive modules and Auslander-Reiten quiver. we give concrete forms and then have a detail proof.In the third part, we introduce the notion of C-flat modules based on the notion of C-injective modules, then we give some properties of C-flat modules and study the relationship of C-flat modules and C-injective modules, at the end of this thesis, we give a method to construct C-flat modules.