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

In this paper, we compute the number of distinct centralizers some classes finite rings. We then characterize all rings with $n$ for any positive integer $n \le 5$. Further give connections between a ring and its commutativity degree.