Research on some generalized extending conditions

In this thesis extending modules, Goldie extending modules and C_11-modules which are the generalizations of the extending modules are examined in detail. For this purpose, the basic notions and theorems used in our study are given in detail in the first chapter. In the second chapter, the required properties of projective, injective and quasi-injective module classes are given along with their proofs. In the third chapter, continuous, quasi-continuous and CS-modules which are the basis of our study are investigated. In the fourth chapter, Goldie extending (G-extending) modules are discussed. In particular, the direct summand of a Goldie extending module and the direct sum of Goldie extending modules are researched. The characterization of this module class is given in detail along with its main properties. In the last chapter, the C_11-module class is emphasized. Unlike the direct sum of C_11-modules, it is shown that the direct summand of a C_11-module need not be a C_11-module. In addition, the results are given for when the direct summand of a C_11-module becomes a C_11-module. Finally, the relationships between the extending, G-extending, C_11 and FI-extending modules are explained.