Abstract

This dissertation investigates the theoretical framework and properties of nil-injective modules and various generalizations of morphic rings. It explores several extensions of p-injective modules, such as nil-injective, Wnil-injective, weakly np-injective, and np-injective modules. It introduces different types of morphic rings, such as right (left) nil-morphic and right (left) np-morphic rings. Special cases of morphic rings, including simple morphic, self-morphic, and unit np-morphic rings, are also discussed. The study begins with an examination of nil-injective modules, presenting non-trivial examples and analysing the relationships between various types of injective modules and morphic rings. A significant part of the study involves designing algorithms to illustrate relationships and derive new results.