Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f,d:R→A are linear maps satisfying thatthen there exist a generalized derivation g:B→AC+C and a linear map ζ:R→C such that f(x)=g(x)+ζ(x) for all x∈R and ζ([R,R])=0 provided that A does not satisfy the standard identity of degree 18.
關聯:
Linear Algebra and its Applications, 430(4): 1236-1242