On generalized Lie derivations of Lie ideals of prime algebras

摘要

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 that f([x,y]) = f(x)y - f(y)x + xd(y) - yd(x) for all x, y is an element of R, then there exist a generalized derivation g : B -> AC + C and a linear map zeta : R - C such that f(x) = g(x) + zeta(x) for all x is an element of R and zeta([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18. (C) 2008 Published by Elsevier Inc.