On The Generalizations Of FG-Modules

The FG-modules play an important role in many parts of ring and categories of modules,so we introduce the notion of generalized FG-projective modules, FG-flat modules and FG-injective modules and study theirs properties. And use them to characterize the rings and FG-dimension.In the first chapter,we introduce the notion of modules,At the same time,we discussed some properties of modules. Then a series of important theorems are given.it is a special type of modules,Furdermore we define a special ring:semisimple ring,we prove some equivalent Propositions of projective modules.In the second chapter,we give a generalization of module,Further, we defined the flat modules and injective modules and scusses some properties of a flat module,using semisimple module class,and then we study the relationship between the flat module and flat module.We introduce the concept flat module and get some properties similar to flat module.In the third chapter,Because of injective dimension and flat dimension is always available and engraved, in this chapter we proved that the injective dimension and flat dimension is portrayed using, so we define the dimension, and made some equivalent characterizations of the dimension.