الملخص

If for any maximal right ideal P of B and a ∈ N(B) ,aB/ aP is almost N-injective, then a ring B is said to be right generalized almost N-injective. In this article, we present some significant findings that are known for right almost N-injective rings and demonstrate that they hold for right generalized almost N-injective rings. At the same time, we study the case in which every S.S.Right B-module is generalized almost N-injective.