Komplekslerde homoloji

In this thesis, we study on the generalizations of the some concepts in the category R-Mod (for ex. Projective module, injective module Ext, complete cotorsion pair, etc.) to the category of complexes on R-Mod. Moreover it is used Enochs? definition for Ext. This definition is different from Foxby and Avramov?s.This thesis consists of four chapters. In the first chapter, the first part contains some basic homological concepts in the category R-Mod and the second part contains some basic concepts in the category of complexes. . In the second chapter, it is studied the relationships between exact complexes and DG-projective and DG-injective complexes. Moreover we see that every complex has an exact cover with kernel DG-injective, an exact envelope with cokernel DG-projective and a DG-injective envelope with cokernel exact. In the third chapter, it is given a necessary condition to be that a quasi-isomorphism is an isomorphism. In the final chapter, if (C,D) is a complete cotorsion pair in the category of complexes such that C is suspension closed, we see that when we regard C and D as subcategories of the homotopy category K(R-Mod), then the embedding functors C ? K(R-Mod) and D ? K(R-Mod) have left and rigt adjoints, respectively.