On Lie Ideals and Automorphisms in Prime Rings

Let R be a prime ring of characteristic different from 2 with center Z and extended centroid C, and let L be a Lie ideal of R. Consider two nontrivial automorphisms alpha and beta of R for which there exist integers m,n >= 1 such that alpha(u)(n) + beta(u)(m) = 0 for all u is an element of L. It is shown that, under these assumptions, either L is central or R subset of M-2(C) (where M-2(C) is the ring of 2 x 2 matrices over C), L is commutative, and u(2) is an element of Z for all u is an element of L. In particular, if L =[R, R], then R is commutative.