Generalized Derivations Acting as Homomorphisms and Anti-Homomorphisms on Lie Ideals of Prime Rings

Abstract

Let U be a non-zero square closed Lie ideal of a 2-torsion free prime ring R and f a generalized derivation of R with the associated derivation d of R. If f acts as a homomorphism and as an antihomomorphism on U, then we prove that, the centre of R.

Derivations on Lie Ideals of σ-Prime Γ-Rings

“…They studied Jordan left derivations on a -square closed Lie ideals and proved that such type of Jordan derivations is a derivation on a -square closed Lie ideals of a -prime -ring. Paul and Chakraborty (2015) studied -prime -rings and proved that if a derivation d acting as homomorphism and an anti-homomorphism in a -Lie ideal U of a -prime -ring M,…”