Some Characterizations on Actions of Generalized Derivations AsHomomorphisms And Anti-Homomorphisms In SemiprimeGamma Rings

Abstract

Let I be a non-zero left ideal of a r-ring M satisfying the condition alpha alpha b beta c= a beta b alpha c for all a,b,c, e M and alpha, beta e r. We show that M contains a non-trivial central ideal if M is semiprime which admits an appropriate non-zero derivations on I, and also that M is commutative if M is prime admitting a non-zero centralizing derivation on I. We next give some characterizations when non-zero generalized derivations act as homomorphisms and as anti-homomorphisms on some non-zero left or two-sided ideals of semiprime gamma rings, somewhere of prime gamma rings also, satisfying the above condition.GANIT J. Bangladesh Math. Soc. 42.1 (2022) 025- 034