$D$-Semiprime Rings

Abstract

Let $R$ be an associative and 2-torsion-free ring with an identity. in this work, we will generaliz 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.