LAUSR

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 α and β of R for which there exist integers m,n ≥ 1 such that α ( u ) n + β ( u ) m = 0 for all u ∈ L . It is shown that, under these assumptions, either L is central or R ⊆ M 2 ( C ) (where M 2 ( C ) is the ring of 2 × 2 matrices over C ), L is commutative, and u 2 ∈ Z for all u ∈ L . In particular, if L =[ R, R ], then R is commutative.