On Lie ideals with derivations as homomorphisms and anti-homomorphisms

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

“…In [2], Bell and Kappe prove that if a derivation acts as a homomorphism and as an anti-homomorphism on a non-zero ideal I of a prime ring R, then 0  d . Asma, Rehman and Shakir [1] extend this result to a square closed Lie ideal, whereas Rehman [8] proves the same result for generalized derivations.…”

$\Gamma^*$-DERIVATION ACTING AS AN ENDOMORPHISM AND AS AN ANTI-ENDOMORPHISM IN SEMIPRIME $\Gamma$-RING M WITH INVOLUTION

“…al. [1] extended this result of prime rings on square closed Lie ideals. Afterwards, the said result was extended to σ-prime rings by Oukhtite et.…”

Generalized Derivations on Prime Near Rings

“…However as noted in [4], the behaviour of is somewhat restricted in the case of a prime ring. Recently the authors in [6] considered ( , )-derivation acting as a homomorphism or an antihomomorphism on a nonzero Lie ideal of a prime ring and concluded that = 0. In this section we establish similar results in the setting of a semigroup ideal of a 3-prime near ring admitting a generalized derivation.…”