Abstract Let η be a prime ideal of an arbitrary ring ζ’s. We study the quotient ring ζ η {} without assuming the primeness of ζ involving prime ideals under the action of multiplicative b -generalized derivations ℱ: ζ → 𝒬 m r F: ₌ₑ satisfying central algebraic identities. We also generalize Herstein’s result I. N. Herstein, A note on derivations, Canad. Math. Bull. 21 1978, 3, 369–370, Theorem 2 in our Theorem 2. 7.
Ahmed et al. (Thu,) studied this question.