Open AccessOn Lie ideals and $ (\sigma, \tau) $-Jordan derivations on prime rings
Author(s) -
Mohammad Ashraf,
Murtaza A. Quadri,
Nadeem ur Rehman
Publication year - 2001
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.32.2001.338
Subject(s) - mathematics , automorphism , prime (order theory) , sigma , ideal (ethics) , prime ring , combinatorics , ring (chemistry) , pure mathematics , physics , chemistry , philosophy , epistemology , quantum mechanics , organic chemistry
Let $ R $ be a prime ring with characteristic different from two and let $ U $ be a Lie ideal of $ R $ such that $ u^2 in U $ for all $ u in U $. Suppose that $ sigma, au $ are automorphisms of $ R $. In the present paper, it is shown that if $ d $ is an additive mapping of $ R $ into itself satisfying $ d (u^2) = d(u) sigma (v) + au (u) d(v) $ for all $ u,v in U $, then $ d(uv) = d(u) sigma (v) + au(u) d(v) $ for all $ u, v in U $.