Nilpotency of Centralizers in Prime Rings

E. C. Posner proved that if λ and δ are derivations of a prime ring R with characteristic not equal 2 , then λδ=0 implies that either λ=0 or δ=0 . David W.Jensen extend this result by showing that , without any characteristic restriction , λδ^m=0 implies either λ=0 or δ^(4m-1)=0 , also he proved that λ^n δ=0 implies either δ^2=0 or λ^(12n-9)=0 , and finally , in general when λ^n δ^m=0 , he showed that if λ and δ are commute , then at least one of the derivations must be nilpotent .Here we ask the possibility if the same results of David can be satisfied on R with replacing the derivations λ andδ with centralizers T and G.