Generalized Lie triple higher derivable maps on rings

Abstract

Let be a ring containing a nontrivial idempotent with the center Z() and ℕ be the set of all non-negative integers. Let Δ = {G_n}_n∈ℕ be a family of mappings G_n : (not necessarily additive) such that , the identity mapping of . Then Δ is said to be a generalized Lie triple higher derivable mapping of holds for all a; b; c ∈ and for each n ∈ ℕ, where is a family of mappings (not necessarily additive) such that satisfying for each n ∈ ℕ, a, b, c ∈ . In the present paper, it is shown that, if is a ring containing a nontrivial idempotent which admits a generalized Lie triple higher derivable mapping Δ = {G_n}n∈ℕ, then there exists an element z_a,b (depending on a and b) in the center Z() such that G_n(a + b) = G_n(a)+ G_n(b)+ z_a,b for all a, b ∈ and for each n ∈ ℕ.

Mathematics Subject Classification (2010):

• 16W25
• 16N60

Key words:

• Derivation
• Lie derivable mappings
• Lie triple higher derivable mappings
• generalized Lie triple higher derivable mappings