COCENTRALIZING DERIVATIONS AND NILPOTENT VALUES ON LIE IDEALS
Articles > Article · 2010
Authors: Nurcan ARGAÇ, Vincenzo De Filippis
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, Journal Indexed in SCI Expanded, International, 2010, vol 41, pp 475-483
DOI: 10.1007/s13226-010-0029-6
Summary
Let R be a prime ring with charR not equal 2, L a non-central Lie ideal of R, d,g non-zero derivations of R, n >= 1 a fixed integer. We prove that if (d(x)x - xg(x))(n) = 0 for all x is an element of L, then either d = g = 0 or R satisfies the standard identity 84 and d, g are inner derivations, induced respectively by the elements a and b such that a + b is an element of Z(R).