Derivations of differentially semiprime rings

Abstract

Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text]. We study Lie rings Der [Formula: see text] in the non-commutative case and prove that if [Formula: see text] is a [Formula: see text]-torsion-free [Formula: see text]-semiprime ring, then [Formula: see text] is a semiprime Lie ring or [Formula: see text] is a commutative ring.

Reverse Derivations on δ-prime rings

“…Many researchers studied the properties of Lie rings with derivations D of differentially simple, prime and semiprime rings (see for example [1][2][3][4], [14,15], [16,17] and [18,28], where further references can be found for the widening in this field.…”