CENTRALIZERS ON SEMIPRIME GAMMA RINGS

Abstract

Let M be a 2-torsion free semiprime Γ-ring satisfying a certain assumption and let T : M → M be an additive mapping such that

         T(xαyβx) = xαT(y)βx

holds for all x, y ∈ M, and α,β ∈ Γ. Then we prove that T is a centralizer.  We also show that T is a centralizer if M contains a multiplicative identity 1.