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.

摘要

让是一个包含非平凡幂等的环，以Z ( )为中心，ℕ 是所有非负整数的集合。令 Δ = { G _n } _n∈ℕ是一个映射族G _n：（不一定相加）使得， 的恒等映射。那么 Δ 被称为对所有a成立的广义 Lie 三重高可导映射；乙; c ∈ 并且对于每个n ∈ ℕ，其中是一个映射族（不一定是可加的），使得满足每个n ∈ ℕ，a, b, c ∈ 。在本文中，表明如果是一个包含非平凡幂等的环，该环允许广义 Lie 三元更高可导映射 Δ = { G _n } n∈ℕ，则存在元素z _a,b（取决于a和b ) 在中心Z ( ) 使得G _n ( a + b ) = G _n ( a )+ G _n ( b )+ z _a,b对于所有a , b ∈ 并且对于每个n ∈ ℕ。