Structure of a quotient ring R/P and its relation with generalized derivations of R

The fundamental aim of this paper is to investigate the structure a quotient ring R/P where R an arbitrary and P prime ideal R. More precisely, we will characterize commutativity via behavior generalized derivations satisfying algebraic identities involving P. Moreover, various wellknown results characterizing (semi-prime) rings have been extended. Furthermore, examples are given prove that restrictions imposed on hypothesis theorems were not superfluous.