@article{2019,title={A RECENT GENERALIZATION OF RAD-SUPPLEMENTING MODULES},abstractNode={In this study, generalized δ-supplementing and ample generalized δ-supplementing modules are defined as a new generalization of Rad-supplementing modules and modules with the property (δ-E) (briefly δ-supplementing) which were studied in (Özdemir, 2016) and (Sözen et. al., 2017) respectively and some basic properties of them are investigated. All rings will be associative with identity and all modules will be unital left modules in this paper. Generalized δ-supplementing modules are of course a generalization of injective modules such as Zöschinger’s modules with the property (E). It is shown that δ-supplementing and δ-radical modules are both δ-supplementing. In general, generalized δ-supplementing modules need not be δ-supplementing. We give an example which supports this reality. Every direct summand of a generalized δ-supplementing module is generalized δ-supplementing. As a useful result, we add that the δ-cover of a generalized δ-supplementing module is also generalized δ-supplementing. Following this, we give an immediate consequence such that every module with composition series is generalized δ-supplementing. Moreover, we prove that generalized δ-supplemented modules are preserved under extensions. We wonder whether the factor module of a generalized δ-supplementing module is also generalized δ-supplementing and so we find a positive answer under a special condition. Moreover, we point the cases being generalized δ-supplementing and injectivity are coincide for modules over δ-V-rings. For a module M, the necessary and sufficient condition of being ample generalized δ-supplementing is that every submodule of M is generalized δ-supplementing. As a result, it is also said that every ample generalized δ-supplementing module is a generalized δ-supplemented module.},author={Figen ERYILMAZ-Esra ÖZTÜRK SÖZEN},year={2019},journal={Turkish Studies-Information Technologies and Applied Sciences}}