An Equations Related to θ-Centralizers on Lie Ideals
Journal of Al-Qadisiyah for Computer Science and Mathematics,
2010, Volume 2, Issue 2, Pages 1-10
AbstractAbstract : 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,: RR are additive mappings, such that 3T(xyx) = T(x)θ(yx) + θ(x)T(y)θ(x) + θ(xy)T(x) and θ(x)T(xy+yx)θ(x) = θ(x)T(y)θ(x2) + θ(x2)T(y)θ(x) holds for all pairs x, y U , if θ is a surjective endomorphism on U, and T(u) U, for all uU, then T(xy)= T(x)θ(y) = θ(x)T(y) for all x,yU.
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