Weakly δ_ss-supplemented modules

The aim of this thesis to construct an algebraic structure between weakly ss-supplemented modules and weakly δ-supplemented modules whose existences are known in the literature. With this scope, the basic algebraic properties of weakly δ_ss-supplemented modules, which are the modules representing the title of thesis, are investigated. Summary, the equivalent conditions are determined for a module to be weakly δ_ss-lifting. In particular, each module providing one of these equivalent conditions are identified as δ_ss-semilocal. A ring R is said to be δ_ss-semilocal if (_R^)R is δ_ss-semilocal. As a consequence, the existence of a subclass of δ-perfect rings is obtained. And some examples are given to show that the inclusion relation is proper between these classes of rings. Moreover, the rings are examined whose modules are all weakly δ_ss-supplemented. It is shown that the concepts of weakly δ_ss-supplemented and amply weakly δ_ss-supplemented modules coincide. The suitable conditions are found for a weakly δ-supplemented module to be weakly δ_ss-supplemented. The class of weakly δ_ss-supplemented modules is closed under direct sums and homomorphic images. And it is proven that a submodule of a weakly δ_ss-supplemented module is weakly δ_ss-supplemented under a suitable condition.