An engel condition with automorphisms for left ideals

Cheng-Kai Liu

Research output: Contribution to journal › Article

10 Citations (Scopus)

Abstract

Let R be a prime ring and L a nonzero left ideal of R. For x, y ∈ R, we denote [x, y] = xy-yx the commutator of x and y. In this paper, we prove that if R admits a non-identity automorphism σ such that [[...[[σ(x n0), xn1], xn2], ...], xnk] = 0 for all x ∈ L, where n0, n1, n2, ..., n k are fixed positive integers, then R is commutative. The analogous results for semiprime rings and von Neumann algebras are also obtained.

Original languageEnglish
Article number1350092
JournalJournal of Algebra and its Applications
Volume13
Issue number2
DOIs
Publication statusPublished - 2014 Mar 1

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Semiprime Ring
Electric commutators
Prime Ring
Von Neumann Algebra
Commutator
Automorphism
Algebra
Automorphisms
Denote
Integer

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics

Cite this

Liu, Cheng-Kai. / An engel condition with automorphisms for left ideals. In: Journal of Algebra and its Applications. 2014 ; Vol. 13, No. 2.
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Liu, C-K 2014, 'An engel condition with automorphisms for left ideals', Journal of Algebra and its Applications, vol. 13, no. 2, 1350092. https://doi.org/10.1142/S0219498813500928

An engel condition with automorphisms for left ideals. / Liu, Cheng-Kai.

In: Journal of Algebra and its Applications, Vol. 13, No. 2, 1350092, 01.03.2014.

Research output: Contribution to journal › Article

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AB - Let R be a prime ring and L a nonzero left ideal of R. For x, y ∈ R, we denote [x, y] = xy-yx the commutator of x and y. In this paper, we prove that if R admits a non-identity automorphism σ such that [[...[[σ(x n0), xn1], xn2], ...], xnk] = 0 for all x ∈ L, where n0, n1, n2, ..., n k are fixed positive integers, then R is commutative. The analogous results for semiprime rings and von Neumann algebras are also obtained.

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Liu C-K. An engel condition with automorphisms for left ideals. Journal of Algebra and its Applications. 2014 Mar 1;13(2). 1350092. https://doi.org/10.1142/S0219498813500928

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