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

【摘要】 <正> 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 s₄-ring,d（x）=[p,x],and g（x）=-d（x）for some p in the Martindalequotient ring of R.更多还原

【Abstract】 Let R be a prime ring of characteristic different from 2,d and g two derivations of R at least one of which is nonzero,L a non-central Lie ideal of R,and a∈R.We prove that if a（d（u）u-ug（u））=0 for any u∈L,then either a=0, or R is an s₄-ring,d（x）=[p,x],and g（x）=-d（x）for some p in the Martindale quotient ring of R.更多还原