Annihilator condition of a pair of derivations in prime and semiprime rings

WOS: 000373307800009Let n be a fixed positive integer, R be a prime ring, D and G two derivations of R and L a noncentral Lie ideal of R. Suppose that there exists 0 not equal a a R such that a(D(u)u (n) -u (n) G(u)) = 0 for all u a L, where n a parts per thousand yen 1 is a fixed integer. Then one of the following holds: D = G = 0, unless R satisfies s (4); char (R) not equal 2, R satisfies s (4), n is even and D = G; char (R) not equal 2, R satisfies s (4), n is odd and D and G are two inner derivations induced by b, c respectively such that b + c a C; char (R) = 2 and R satisfies s (4). We also investigate the case when R is a semiprime ring.National Board for Higher Mathematics (NBHM), India [NBHM/R.P. 26/2012/Fresh/1745]; Scientific and Technological Research Council of Turkey, TUBITAKTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [110T586]This work is supported by a grant from National Board for Higher Mathematics (NBHM), India. Grant No. is NBHM/R.P. 26/2012/Fresh/1745 dated 15.11.12 and second author is supported by The Scientific and Technological Research Council of Turkey, TUBITAK, No. 110T58