T-Commuting Generalized Derivations on Ideals and Semi-Prime Ideal

This paper's primary goal is to look at a quotient ring A/T structure, where A is an arbitrary ring and T is a semi-prime ideal of A. More precisely, we examine the differential identities in a semi-prime ideal of an arbitrary ring involving T-commuting generalized derivation. Furthermore, examples are given to prove that the restrictions imposed on the hypothesisof the various theorems were not superfluous.