Annihilators of power values of derivations in prime rings
Journal
Communications in Algebra
Journal Volume
26
Journal Issue
7
Pages
2091-2113
Date Issued
1998
Author(s)
Chang, C.-M.
Abstract
Abstract In this paper we prove some results concerning annihilators of power values of derivations in prime rings. The following main theorem establishes a unified version of several earlier results in the literature:Let R be a prime ring with center Z and with extended centroid C,Q, its two-sided Martindale quotient ring, �l a nonzero right ideal of R and D a nonzero derivation of R.Suppose that aD([x,y])n ? Z (D([x,y])na ? Z) for all x,y?�l where a?Rand n is a fixed positive integer. If [�l,�l]�l �� 0 and dim C RC >4, then either aD(�l) = 0 (a = 0 resp.) or D= ad(p) for some p? Qsuch that p�l = 0.
Type
journal article