On centralizing automorphisms and Jordan left derivations on σ-prime gamma rings

Abstract

Let M be a 2-torsion free σ-prime Γ-ring and U be a non-zero σ-square closed Lie ideal of M. If T : M → M is an automorphism on U such that T ?= 1 and Tσ = σT on U, then we prove that U ⊆ Z(M). We also study the additive maps d :M → M such that d(uαu) = 2uαd(u), where u ∈ U and α ∈Γ, and show that d(uαv) = uαd(v)+vαd(u), for all u,v ∈ U and α ∈Γ. 2000 AMS Classification: 16W10, 16W25, 16W20, 16U80.