Product of generalized derivations of order 2 with derivations acting on multilinear polynomials with centralizing conditions

Abstract

Let R be a prime ring with char(R) 6= 2. Suppose that f(x1,... , xn) be a noncentral multilinear polynomial over C, G be nonzero generalized derivation of R and d a nonzero derivation of R. In this paper we describe all possible forms of G in the given case.