Abstract:

Let R be a prime ring with a generalized derivationδ and m,n,p∈〖KX,1〗N. Using GPI theory, under the assumption that either 6 is not a common divisor of m and n, or p=1, the authors have proved that ［δ(x),δ(y)］=［x^m,yⁿ］p for all x,y∈R if and only if δ(x)=x or δ(x)=-x, and m=n=p=1.

Key words:  prime ring, generalized derivation, strong commutativity preserving map