On some gamma modules

The aim of this thesis is to investigate the algebraic structure of gamma modules and to obtain the fundamental theorems of free gamma modules, projective gamma modules and injective gamma modules. For this purpose, the definition of linear independence in gamma modules has been redefined and accordingly, new features have been proved in the gamma module structure. This study consists of five chapters. In the first chapter, some information about gamma modules in the literature is given. In the second chapter, definitions and properties that form the basis of gamma rings and gamma modules used in this study are given. In the third chapter, the definition of strong unitary gamma module on gamma ring with strong unity is given. Gamma modules are examined, isomorphism theorems are given, and some basic theorems about gamma module sequences are proved. In the fourth chapter, by defining a subset of a gamma module to be linearly independent and to be a generator, the concept of basis is introduced. Using these concepts, the characterization of free gamma modules is given and some theorems about free gamma modules are proved. Also, some theorems about the basis of vector spaces defined on division gamma rings with strong unity are given. In the fifth chapter, projective and injective gamma modules are defined and characterizations of these modules are given.