DG-Ding Injective And Projective Complexes And Dimensions

In this thesis,we mainly study the DG-Ding injective and DG-Ding projective complexes and dimensions.The whole thesis is made up of three parts.Firstly,we introduce the concepts of DG-Ding injetive and DG-Ding projective complexes,based on the importance of the relationship between complexes and their terms,circles and boundaries in the category of complexes,we establish the relationship between DG-Ding injective(respectively,DG-Ding projective)complexes and their terms,circles and boundaries,which provides an important way to explore the properties of complexes through the properties of modules.Secondly,we study the stability of DG-Ding injective and DG-Ding projective complexes.It is shown that the procedure we used to define the DG-Ding injective complexes yields exactly the DG-Ding injective complexes.Dually,we get the stability of DG-Ding projective complexes.Finally,we define and study the notion of DG-Ding injective dimension and DG-Ding projective dimension of complexes and give a characterization of these dimensions using Ext functors.