A note on generalized derivations with multilinear polynomials in prime rings. Issue 4 (2nd April 2020) - Tiwari, Shailesh Kumar; Singh, Sanjay Kumar
Abstract: Let R be a prime ring of characteristic different from 2, U the Utumi quotient ring of R with the extended centroid C and f ( x 1, …, x n ) be a non-central multilinear polynomial over C . Suppose that F and G are two generalized derivations on R such that F 2 ( u ) u − G ( u 2 ) ∈ C for all u = f ( r 1, …, r n ), then we give the complete description of the mappings F and G .