On Prime Rings with Derivations

This paper identifies all derivations associated with two well-known non-commutative prime rings and provides some remarks on one of these derivations, called the prime derivation. Also, it presents two results for some classes of non-commutative prime rings, regarding when the images of derivations on these rings are subrings of them. The paper also includes some illustrative examples and concludes with a set of questions for further exploration of this topic.