Two Kinds Of Generalized Projective Modules

Projective modules are important research objects in the representation theory and homological algebras,and their properties are one of the most fundamental and central contents in the homological algebras. With the development of homological algebras, various generalizations of projective modules are introduced, and they were widely investigated by many authors.In this thesis, we mainly discuss several different generalizations of projective modules, consisting of relative projective modules and generalized projective modules. Most of the results in the paper are well known. The thesis has three parts.The first part deals with the background and development of relative and generalized projective modules, and we list the main work of this thesis.The second part mainly introduces three relative projective modules. Firstly, we introduce relative FP-projective module and its properties when basic ring is coherent. Secondly, we introduce (n,d)-projective modules, and the relation between (n,d)-projective module and (n,d)-injective module is given. Finally, Gorenstein projective modules are discussed and we get that the class of Gorenstein projective modules is projective resolving.In the third part, we mainly introduce three kinds of generalized projective modules, say P-projective modules, Quasi-projective modules and A-Ker-projective modules. Some properties of them are given and the relation between projective modules and other several generalized projective modules are discussed.