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AN ENGEL CONDITION WITH AUTOMORPHISMS FOR LEFT IDEALS

CHENG-KAI LIU

Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan

https://doi.org/10.1142/S0219498813500928Cited by:9 (Source: Crossref)

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), x^n₁], x^n₂], …], x^n_k] = 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.

Keywords:

AMSC: 16N60, 16W20, 46L40, 46L10

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