Annihilators of Skew Derivations with Engel Conditions on Lie Ideals

Ming Chu Chou, Cheng-Kai Liu

Research output: Contribution to journalArticle

1 Citation (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 languageEnglish
Pages (from-to)898-911
Number of pages14
JournalCommunications in Algebra
Volume44
Issue number2
DOIs
Publication statusPublished - 2016 Feb 1

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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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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.",
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Annihilators of Skew Derivations with Engel Conditions on Lie Ideals. / Chou, Ming Chu; Liu, Cheng-Kai.

In: Communications in Algebra, Vol. 44, No. 2, 01.02.2016, p. 898-911.

Research output: Contribution to journalArticle

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