Rings whose proper cyclic modules are images of injectives

In this thesis, we study the structure of rings over which certain cyclic modules are homomorphic image of injective modules. After presenting the motivational background and some preliminaries, we consider the case when every nonprojective cyclic is the image of an injective module. Then we narrow our focus to the closed specific case where proper cyclic modules satisfy the said property. We obtain some structure theorems about both classes of rings and apply them to the Artin algebra case. It turns out that an Artin algebra satisfying any of these conditions is Quasi-Frobenius, that is, a right self-injective right Artinian ring.