Gorenstein Projective Modules And Gorenstein Projective Complexes

In this thesis, the properties of Gorenstein projective modules on general associative rings are investigated. We study Gorenstein projective complexes on Gorenstein rings, and the relationship between Gorenstein projective mod-ules and Gorenstein projective complexes. It consists of the following three parts.In the first chapter, we introduce the background and the signification of our main work, some notations and notions in this thesis.The chapter 2, we introduce some related notions on Gorenstein homo-logical algebras, and focus on the Gorenstein projective modules, projectively resolving classes, proper left projective resolution and coproper right projec-tive resolution. It is well-known that the class of all Gorenstein projective modules is projectively resolving, and the class of all Gorenstein projective modules is closed under the direct sums and direct summands. In addition, some properties of Gorenstein projective dimensions are discussed.Chapter 3 introduce the notion of Gorenstein projective complexes, and some properties of Gorenstein projective complexes on Gorenstein rings. Fur-thermore, we prove that each term Cm (m∈Z) of a Gorenstein projective com-plex C over an arbitrary ring R is Gorenstein projective module, which partly generalize some conclusions of Gorenstein projective complexes on Gorenstein rings. Finally, we give the relation between Gorenstein projective complex C and the cosyzygy L of any projective complex, says Exti(C, L)=0.