On generalized derivations and commutativity of prime rings with involution

Abstract

Let R be a ring with involution *. A map δ of the ring R into itself is called a derivation if δ(xy) = δ(x)y + xδ(y) for all x, y ∈ R. An additive map F : R → R is called a generalized derivation on R if F(xy) = F(x)y + xδ(y) for all x, y ∈ R,

On Commutativity of Semiprime Rings with Multiplicative (Generalized)-derivations

“…In the literature, a number of authors have discussed the commutativity of prime rings and semiprime rings admitting derivations and generalized derivations satisfying certain algebraic identities, see (Ali, Kumar & Miyan, 2011), (Ali, Dhara & Fosner, 2011), (Andima & Pajoohesh, 2010), (Ashraf et al, 2007(Ashraf et al, , 2001, (Daif & Bell, 1992), (Dhara & Pattanayak, 2011), (Hongan, 1997), where further references can be found.…”

Generalized derivations on Lie ideals in prime rings

“…Several authors [1,2,5,13,14], have studied these identities on some appropriate subsets of prime, semiprime rings. Recently, Dhara et al [10], studied these identities on Lie ideals.…”