D-Semiprime Rings (European Journal of Pure and Applied Mathematics, 2024)
Let R be an associative and 2-torsion-free ring with an identity. in this work, we will generalize the results of differentially prime rings in [18] by applying the hypotheses in a differentially semiprime rings. In particular, we have proved that if R is a D-semiprime ring, then either R is a commutative ring or D is a semiprime ring.
Keywords: Derivation, semiprime ring, Lie Ideal, Jordan Ideal