Commutative radical rings. II.
In this paper we investigate commutativity of ring with involution which admits a derivation satisfying certain algebraic identities on Jordan ideals of . Some related results for prime rings are also discussed. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.
We discuss range inclusion results for derivations on noncommutative Banach algebras from the point of view of ring theory.