# Annihilators of Skew Derivations with Engel Conditions on Lie Ideals

Ming Chu Chou, Cheng-Kai Liu

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

Let R be a prime ring, L a noncentral Lie ideal of R, and a ∈ R. Set [x, y]1 = [x, y] = xy − yx for x, y ∈ R and inductively [x, y]k = [[x, y]k−1, y] for k > 1. Suppose that δ is a nonzero σ-derivation of R such that a[δ(x), x]k = 0 for all x ∈ L, where σ is an automorphism of R and k is a fixed positive integer. Then a = 0 except when char R = 2 and R ⊆ M2(F), the 2 × 2 matrix ring over a field F.

Original language English 898-911 14 Communications in Algebra 44 2 https://doi.org/10.1080/00927872.2014.990028 Published - 2016 Feb 1

Skew Derivation
Lie Ideal
Matrix Ring
Prime Ring
Annihilator
Automorphism
Integer

### All Science Journal Classification (ASJC) codes

• Algebra and Number Theory

### Cite this

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title = "Annihilators of Skew Derivations with Engel Conditions on Lie Ideals",
abstract = "Let R be a prime ring, L a noncentral Lie ideal of R, and a ∈ R. Set [x, y]1 = [x, y] = xy − yx for x, y ∈ R and inductively [x, y]k = [[x, y]k−1, y] for k > 1. Suppose that δ is a nonzero σ-derivation of R such that a[δ(x), x]k = 0 for all x ∈ L, where σ is an automorphism of R and k is a fixed positive integer. Then a = 0 except when char R = 2 and R ⊆ M2(F), the 2 × 2 matrix ring over a field F.",
author = "Chou, {Ming Chu} and Cheng-Kai Liu",
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In: Communications in Algebra, Vol. 44, No. 2, 01.02.2016, p. 898-911.

Research output: Contribution to journalArticle

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T1 - Annihilators of Skew Derivations with Engel Conditions on Lie Ideals

AU - Chou, Ming Chu

AU - Liu, Cheng-Kai

PY - 2016/2/1

Y1 - 2016/2/1

N2 - Let R be a prime ring, L a noncentral Lie ideal of R, and a ∈ R. Set [x, y]1 = [x, y] = xy − yx for x, y ∈ R and inductively [x, y]k = [[x, y]k−1, y] for k > 1. Suppose that δ is a nonzero σ-derivation of R such that a[δ(x), x]k = 0 for all x ∈ L, where σ is an automorphism of R and k is a fixed positive integer. Then a = 0 except when char R = 2 and R ⊆ M2(F), the 2 × 2 matrix ring over a field F.

AB - Let R be a prime ring, L a noncentral Lie ideal of R, and a ∈ R. Set [x, y]1 = [x, y] = xy − yx for x, y ∈ R and inductively [x, y]k = [[x, y]k−1, y] for k > 1. Suppose that δ is a nonzero σ-derivation of R such that a[δ(x), x]k = 0 for all x ∈ L, where σ is an automorphism of R and k is a fixed positive integer. Then a = 0 except when char R = 2 and R ⊆ M2(F), the 2 × 2 matrix ring over a field F.

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