An Equations Related to Î¸-Centralizers on Lie Ideals - H. Majeed, Abdulrahman; I. Meften, Mushreq (Journal of Al-Qadisiyah for Computer Science and Mathematics, 2017)
The purpose of this paper is to prove the following result : Let R be a 2-torsion free prime ring , U a square closed Lie ideal, and T,ï±: Rï‚®R are additive mappings, such that 3T(xyx) = T(x)Î¸(yx) + Î¸(x)T(y)Î¸(x) + Î¸(xy)T(x) and Î¸(x)T(xy+yx)Î¸(x) = Î¸(x)T(y)Î¸(x2) + Î¸(x2)T(y)Î¸(x) holds for all pairs x, y ïƒŽ U , if Î¸ is a surjective endomorphism on U, and T(u) ïƒŽU, for all uïƒŽU, then T(xy)= T(x)Î¸(y) = Î¸(x)T(y) for all x,yïƒŽU.