Generalized ADS modules with the SIP

In 1970, Fuchs defined modules for the absolute direct summand property (Ads) in recent years is a subject of popular research. After defining the summand intersection property (SIP) for Wilson modules in 1986, many mathematicians have done many researches on this feature and still do it. Although these two concepts seem to be connected, they are completely different concepts. In 2015, Takıl Mutlu added the concept of SA-module, which is a new module class that provides both Ads and SIP property. In this thesis, a generalization of the class of modules that provides Ads and SIP property is made. Firstly, basic notions and theorems in the module theory which will be used in this work are given. Then, some of the properties of the class of module that provides the Ads and SIP property known as SA modules are given with their proofs. Finally, SA-extending modules, as a generalization of SA modules, are defined. Necessary and sufficient conditions for a module on an arbitrary ring to be SA-extending are given. Also a condition for the direct sum of two SA-extending modules to be an SA-extending module is provided.