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

Year 2015, Volume: 44 Issue: 1, 51 - 57, 08.06.2020

Kalyan Kumar Dey Akhil Chandra Paul Bijan Davvaz

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 6= 1 and T σ = 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.

Keywords

σ-prime Γ-ring, centralizing automorphisms, Lie ideals, left derivations, Jordan left derivations

References

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