On Generalized Simple Singular AP-Injective Rings

A ring R is said to be generalized right simple singular AP-injective, if for any maximal essential right ideal M of R and for any bM, bR/bM is AP-injective. We shall study the characterization and properties of this class of rings. Some interesting results on these rings are obtained. In particular, conditions under which generalized simple singular AP-injective rings are weakly regular rings, and Von Neumann regular rings.