Annihilator on Co-commutators with Derivations on Lie Ideals in Prime Rings

摘要

Let R be a prime ring of characteristic different from 2,d and g twoderivations of R at least one of which is nonzero,L a non-central Lie ideal of R,anda∈R.We prove that if a(d(u)u-ug(u))=0 for any u∈L,then either a=0,or R is an s_4-ring,d(x)=[p,x],and g(x)=-d(x)for some p in the Martindalequotient ring of R.