On modules with the absolute direct summand property

ABSTRACT Master of Science Thesis ON MODULES WITH THE ABSOLUTE DIRECT SUMMAND PROPERTY FİGEN TAKIL Anadolu University Graduate School of Natural and Applied Sciences Mathematics Program Supervisor: Prof. Dr. Adnan TERCAN 2003, 53 Pages In this thesis, the structural properties of modules with the Absolute Direct Summand Property (ADS) were examined. Firstly, basic notions and theorems in the module theory which will be used in this work were also presented. Then the neccessary properties of the classes of modules which known as CS (Extending) and Quasi-Continuous in the literature were given with their proofs. Finally, neccessary and sufficient conditions for a module on an arbitrary ring to have the absolute direct summand property were given. Then the properties which are provided on ADS modules defined on a Noetherian ring were examined. It was shown with examples that the family of ADS modules is independent off the family of SIP modules. Keywords: CS, Quasi-Continuous Module, Ads-Module, Essential and Complement Submodule, Injective ve Relatively Injective Module 11