b-Generalized derivations act as a multipliers on prime rings

Abstract

Let R be a prime ring of characteristic different from 2, U be its Utumi quotient ring with the extended centroid C and $f(x_1,\dots ,x_n)$ be a non-central multilinear polynomial over C. Suppose that F, G and H are b-generalized derivations on R such that $$F(f(r))f(r)-f(r)G(f(r))=H(f{(r)}^2)$$ for all $r\in R^n,$ then we describe all possible forms of F, G and H.

Keywords:

• Left multipliers
• b-generalized derivations
• multilinear polynomials
• prime rings
• Utumi quotient ring
• extended centroid

2020 Mathematics Subject Classification:

• 16N60
• 16W25